diff --git a/Pantograph/Goal.lean b/Pantograph/Goal.lean
index a546d49..1b9ab12 100644
--- a/Pantograph/Goal.lean
+++ b/Pantograph/Goal.lean
@@ -22,8 +22,9 @@ structure GoalState where
   -- Parent state metavariable source
   parentMVar?: Option MVarId := .none
 
-  -- If this is not `.none` there is a partial tactic being executed
-  fragment? : Option TacticFragment := .none
+  -- Any goal associated with a fragment has a partial tactic which has not
+  -- finished executing.
+  fragments : FragmentMap := .empty
 
 @[export pantograph_goal_state_create_m]
 protected def GoalState.create (expr: Expr): Elab.TermElabM GoalState := do
@@ -95,16 +96,12 @@ private def GoalState.restoreTacticM (state: GoalState) (goal: MVarId): Elab.Tac
 
 @[export pantograph_goal_state_focus]
 protected def GoalState.focus (state : GoalState) (goal : MVarId): Option GoalState := do
-  let fragment? := match state.fragment? with
-    | .some { goal := goal', .. } => if goal' == goal then state.fragment? else .none
-    | .none => .none
   return {
     state with
     savedState := {
       state.savedState with
       tactic := { goals := [goal] },
     },
-    fragment?,
   }
 
 /-- Immediately bring all parent goals back into scope. Used in automatic mode -/
@@ -125,10 +122,10 @@ protected def GoalState.immediateResume (state: GoalState) (parent: GoalState):
   }
 
 /--
-Brings into scope a list of goals. User must ensure `goals` is distinct.
+Brings into scope a list of goals. User must ensure `goals` are distinct.
 -/
 @[export pantograph_goal_state_resume]
-protected def GoalState.resume (state: GoalState) (goals: List MVarId): Except String GoalState := do
+protected def GoalState.resume (state : GoalState) (goals : List MVarId) : Except String GoalState := do
   if ¬ (goals.all (λ goal => state.mvars.contains goal)) then
     let invalid_goals := goals.filter (λ goal => ¬ state.mvars.contains goal) |>.map (·.name.toString)
     .error s!"Goals {invalid_goals} are not in scope"
@@ -147,7 +144,7 @@ protected def GoalState.resume (state: GoalState) (goals: List MVarId): Except S
 Brings into scope all goals from `branch`
 -/
 @[export pantograph_goal_state_continue]
-protected def GoalState.continue (target: GoalState) (branch: GoalState): Except String GoalState :=
+protected def GoalState.continue (target : GoalState) (branch : GoalState) : Except String GoalState :=
   if !target.goals.isEmpty then
     .error s!"Target state has unresolved goals"
   else if target.root != branch.root then
@@ -156,7 +153,7 @@ protected def GoalState.continue (target: GoalState) (branch: GoalState): Except
     target.resume (goals := branch.goals)
 
 @[export pantograph_goal_state_root_expr]
-protected def GoalState.rootExpr? (goalState : GoalState): Option Expr := do
+protected def GoalState.rootExpr? (goalState : GoalState) : Option Expr := do
   if goalState.root.name == .anonymous then
     .none
   let expr ← goalState.mctx.eAssignment.find? goalState.root
@@ -452,14 +449,21 @@ protected def GoalState.tryTacticM
 protected def GoalState.tryTactic (state: GoalState) (goal: MVarId) (tactic: String):
     Elab.TermElabM TacticResult := do
   state.restoreElabM
-  if let .some { goal := goal', fragment } := state.fragment? then
-    if goal == goal' then
-      return ← withCapturingError do
-        let (fragment?', state') ← state.step' goal (fragment.step goal tactic)
-        return { state' with fragment? := fragment?' }
+  /-
+  if let .some fragment := state.fragments[goal]? then
+    return ← withCapturingError do
+      let (moreFragments, state') ← state.step' goal (fragment.step goal tactic)
+      let fragments := moreFragments.fold (init := state.fragments.erase goal) λ acc mvarId f =>
+        acc.insert mvarId f
+      return { state' with fragments } -/
+
+  let catName := match isLHSGoal? (← goal.getType) with
+    | .some _ => `conv
+    | .none => `tactic
+  -- Normal tactic without fragment
   let tactic ← match Parser.runParserCategory
     (env := ← MonadEnv.getEnv)
-    (catName := `tactic)
+    (catName := catName)
     (input := tactic)
     (fileName := ← getFileName) with
     | .ok stx => pure $ stx
@@ -468,6 +472,8 @@ protected def GoalState.tryTactic (state: GoalState) (goal: MVarId) (tactic: Str
   withCapturingError do
     state.step goal tacticM (guardMVarErrors := true)
 
+-- Specialized Tactics
+
 protected def GoalState.tryAssign (state: GoalState) (goal: MVarId) (expr: String):
       Elab.TermElabM TacticResult := do
   state.restoreElabM
@@ -480,8 +486,6 @@ protected def GoalState.tryAssign (state: GoalState) (goal: MVarId) (expr: Strin
     | .error error => return .parseError error
   state.tryTacticM goal $ Tactic.evalAssign expr
 
--- Specialized Tactics
-
 protected def GoalState.tryLet (state: GoalState) (goal: MVarId) (binderName: String) (type: String):
       Elab.TermElabM TacticResult := do
   state.restoreElabM
@@ -495,55 +499,49 @@ protected def GoalState.tryLet (state: GoalState) (goal: MVarId) (binderName: St
   state.tryTacticM goal $ Tactic.evalLet binderName.toName type
 
 /-- Enter conv tactic mode -/
-protected def GoalState.conv (state: GoalState) (goal: MVarId):
+@[export pantograph_goal_state_conv_enter_m]
+protected def GoalState.conv (state : GoalState) (goal : MVarId) :
       Elab.TermElabM TacticResult := do
-  if state.fragment? matches .some { fragment := .conv .., .. } then
+  if let .some (.conv ..) := state.fragments[goal]? then
     return .invalidAction "Already in conv state"
   goal.checkNotAssigned `GoalState.conv
   withCapturingError do
     let (fragment, state') ← state.step' goal Fragment.enterConv
-    let fragment? := .some {
-      goal := state'.goals[0]!,
-      fragment,
-    }
     return {
       state' with
-      fragment?
+      fragments := state'.fragments.insert goal fragment
     }
 
 /-- Exit from `conv` mode. Resumes all goals before the mode starts and applys the conv -/
 @[export pantograph_goal_state_conv_exit_m]
-protected def GoalState.convExit (state: GoalState):
+protected def GoalState.convExit (state : GoalState) (goal : MVarId):
       Elab.TermElabM TacticResult := do
-  let .some { goal, fragment } := state.fragment? |
-    return .invalidAction "Not in conv state"
-  unless fragment matches .conv .. do
+  let .some fragment@(.conv ..) := state.fragments[goal]? |
     return .invalidAction "Not in conv state"
   withCapturingError do
-    let state' ← state.step goal (fragment.exit goal)
+    let (fragments, state') ← state.step' goal (fragment.exit goal state.fragments)
     return {
       state' with
-      fragment? := .none,
+      fragments,
     }
 
-protected def GoalState.calcPrevRhsOf? (state: GoalState) (goal: MVarId): Option Expr := do
-  match state.fragment? with
-  | .some { goal := goal', fragment := .calc prevRhs? } =>
-    if goal == goal' then prevRhs? else .none
-  | .some _ => unreachable!
-  | .none => .none
+protected def GoalState.calcPrevRhsOf? (state : GoalState) (goal : MVarId) : Option Expr := do
+  let .some (.calc prevRhs?) := state.fragments[goal]? | .none
+  prevRhs?
 
 @[export pantograph_goal_state_try_calc_m]
-protected def GoalState.tryCalc (state: GoalState) (goal: MVarId) (pred: String):
-      Elab.TermElabM TacticResult := do
+protected def GoalState.tryCalc (state : GoalState) (goal : MVarId) (pred : String)
+  : Elab.TermElabM TacticResult := do
   let prevRhs? := state.calcPrevRhsOf? goal
   withCapturingError do
-    let (fragment?, state') ← state.step' goal do
+    let (moreFragments, state') ← state.step' goal do
       let fragment := Fragment.calc prevRhs?
       fragment.step goal pred
+    let fragments := moreFragments.fold (init := state.fragments.erase goal) λ acc mvarId f =>
+      acc.insert mvarId f
     return {
       state' with
-      fragment?,
+      fragments,
     }
 
 end Pantograph
diff --git a/Pantograph/Serial.lean b/Pantograph/Serial.lean
index ce352d6..0dab926 100644
--- a/Pantograph/Serial.lean
+++ b/Pantograph/Serial.lean
@@ -104,7 +104,7 @@ def goalStatePickle (goalState : GoalState) (path : System.FilePath) : IO Unit :
     }
     root,
     parentMVar?,
-    fragment?,
+    fragments,
   } := goalState
   Pantograph.pickle path (
     env.constants.map₂,
@@ -116,7 +116,7 @@ def goalStatePickle (goalState : GoalState) (path : System.FilePath) : IO Unit :
 
     root,
     parentMVar?,
-    fragment?,
+    fragments,
   )
 
 @[export pantograph_goal_state_unpickle_m]
@@ -132,7 +132,7 @@ def goalStateUnpickle (path : System.FilePath) (env : Environment)
 
     root,
     parentMVar?,
-    fragment?,
+    fragments,
   ), region) ← Pantograph.unpickle (
     PHashMap Name ConstantInfo ×
 
@@ -143,7 +143,7 @@ def goalStateUnpickle (path : System.FilePath) (env : Environment)
 
     MVarId ×
     Option MVarId ×
-    Option TacticFragment
+    FragmentMap
   ) path
   let env ← env.replay (Std.HashMap.ofList map₂.toList)
   let goalState := {
@@ -163,7 +163,7 @@ def goalStateUnpickle (path : System.FilePath) (env : Environment)
     },
     root,
     parentMVar?,
-    fragment?,
+    fragments,
   }
   return (goalState, region)
 
diff --git a/Pantograph/Tactic/Fragment.lean b/Pantograph/Tactic/Fragment.lean
index 296e348..0fbbb03 100644
--- a/Pantograph/Tactic/Fragment.lean
+++ b/Pantograph/Tactic/Fragment.lean
@@ -15,42 +15,50 @@ namespace Pantograph
 inductive Fragment where
   | calc (prevRhs? : Option Expr)
   | conv (rhs : MVarId) (dormant : List MVarId)
+  deriving BEq
+abbrev FragmentMap := Std.HashMap MVarId Fragment
+def FragmentMap.empty : FragmentMap := Std.HashMap.emptyWithCapacity 2
 
 protected def Fragment.enterCalc : Elab.Tactic.TacticM Fragment := do
   return .calc .none
 protected def Fragment.enterConv : Elab.Tactic.TacticM Fragment := do
   let goal ← Elab.Tactic.getMainGoal
-  let convGoal ← goal.withContext do
+  let rhs ← goal.withContext do
     let (rhs, newGoal) ← Elab.Tactic.Conv.mkConvGoalFor (← Elab.Tactic.getMainTarget)
     Elab.Tactic.replaceMainGoal [newGoal.mvarId!]
     pure rhs.mvarId!
   let otherGoals := (← Elab.Tactic.getGoals).filter (· != goal)
-  return .conv convGoal otherGoals
+  return conv rhs otherGoals
 
-protected def Fragment.exit (fragment : Fragment) (goal: MVarId) : Elab.Tactic.TacticM Unit :=
+protected def Fragment.exit (fragment : Fragment) (goal : MVarId) (fragments : FragmentMap)
+  : Elab.Tactic.TacticM FragmentMap :=
   match fragment with
-  | .calc _prevRhs? => Elab.Tactic.setGoals [goal]
+  | .calc .. => do
+    Elab.Tactic.setGoals [goal]
+    return fragments.erase goal
   | .conv rhs otherGoals => do
+    -- FIXME: Only process the goals that are descendants of `goal`
+    let goals := (← Elab.Tactic.getGoals).filter λ goal => true
+      --match fragments[goal]? with
+      --| .some f => fragment == f
+      --| .none => false -- Not a conv goal from this
     -- Close all existing goals with `refl`
-    for mvarId in (← Elab.Tactic.getGoals) do
+    for mvarId in goals do
       liftM <| mvarId.refl <|> mvarId.inferInstance <|> pure ()
     Elab.Tactic.pruneSolvedGoals
-    unless (← Elab.Tactic.getGoals).isEmpty do
-      throwError "convert tactic failed, there are unsolved goals\n{Elab.goalsToMessageData (← Elab.Tactic.getGoals)}"
+    unless (← goals.filterM (·.isAssignedOrDelayedAssigned)).isEmpty do
+      throwError "convert tactic failed, there are unsolved goals\n{Elab.goalsToMessageData (goals)}"
 
     Elab.Tactic.setGoals $ [goal] ++ otherGoals
     let targetNew ← instantiateMVars (.mvar rhs)
     let proof ← instantiateMVars (.mvar goal)
 
     Elab.Tactic.liftMetaTactic1 (·.replaceTargetEq targetNew proof)
-
-structure TacticFragment where
-  -- The goal which the fragment acts on
-  goal : MVarId
-  fragment : Fragment
+    return fragments.erase goal
 
 protected def Fragment.step (fragment : Fragment) (goal : MVarId) (s : String)
-  : Elab.Tactic.TacticM (Option TacticFragment) := goal.withContext do
+  : Elab.Tactic.TacticM FragmentMap := goal.withContext do
+  assert! ¬ (← goal.isAssigned)
   match fragment with
   | .calc prevRhs? => do
     let .ok stx := Parser.runParserCategory
@@ -103,16 +111,9 @@ protected def Fragment.step (fragment : Fragment) (goal : MVarId) (s : String)
     let goals := [ mvarBranch ] ++ remainder?.toList
     Elab.Tactic.setGoals goals
     match remainder? with
-    | .some goal => return .some { goal, fragment := .calc (.some rhs) }
-    | .none => return .none
-  | fragment@(.conv _ _) => do
-    let .ok tactic := Parser.runParserCategory
-      (env := ← MonadEnv.getEnv)
-      (catName := `conv)
-      (input := s)
-      (fileName := ← getFileName) | throwError "Could not parse `conv tactic {s}"
-    Elab.Tactic.evalTactic tactic
-    let goal ← Elab.Tactic.getMainGoal
-    return .some { goal, fragment }
+    | .some goal => return FragmentMap.empty.insert goal $ .calc (.some rhs)
+    | .none => return .empty
+  | .conv .. => do
+    throwError "Direct operation on conversion tactic parent goal is not allowed"
 
 end Pantograph
diff --git a/Repl.lean b/Repl.lean
index d81cc4c..a2cada2 100644
--- a/Repl.lean
+++ b/Repl.lean
@@ -303,6 +303,7 @@ def execute (command: Protocol.Command): MainM Json := do
     let state ← getMainState
     let .some goalState := state.goalStates[args.stateId]? |
       Protocol.throw $ errorIndex s!"Invalid state index {args.stateId}"
+    -- FIXME: Allow proper conversion tactic exit even in automatic mode
     let .some goal := goalState.goals[args.goalId]? |
       Protocol.throw $ errorIndex s!"Invalid goal index {args.goalId}"
     let nextGoalState?: Except _ TacticResult ← liftTermElabM do
@@ -323,7 +324,7 @@ def execute (command: Protocol.Command): MainM Json := do
       | .none, .none, .none, .none, .none, .some true, .none => do
         pure <| Except.ok <| ← goalState.conv goal
       | .none, .none, .none, .none, .none, .some false, .none => do
-        pure <| Except.ok <| ← goalState.convExit
+        pure <| Except.ok <| ← goalState.convExit goal
       | .none, .none, .none, .none, .none, .none, .some draft => do
         pure <| Except.ok <| ← goalState.tryDraft goal draft
       | _, _, _, _, _, _, _ =>
diff --git a/Test/Proofs.lean b/Test/Proofs.lean
index 7f61e16..f8f1f3f 100644
--- a/Test/Proofs.lean
+++ b/Test/Proofs.lean
@@ -362,6 +362,7 @@ def test_conv: TestM Unit := do
   addTest $ LSpec.check tactic ((← state1.serializeGoals (options := ← read)).map (·.devolatilize) =
     #[interiorGoal [] "a + b + c1 = b + a + c2"])
 
+  let goalConv := state1.goals[0]!
   let state2 ← match ← state1.conv (state1.get! 0) with
     | .success state _ => pure state
     | other => do
@@ -433,7 +434,7 @@ def test_conv: TestM Unit := do
   addTest $ LSpec.check s!"  · {convTactic}" ((← state6.serializeGoals (options := ← read)).map (·.devolatilize) =
     #[])
 
-  let state1_1 ← match ← state6.convExit with
+  let state1_1 ← match ← state6.convExit goalConv with
     | .success state _ => pure state
     | other => do
       addTest $ assertUnreachable $ other.toString
diff --git a/doc/repl.md b/doc/repl.md
index aa2d5fa..180505c 100644
--- a/doc/repl.md
+++ b/doc/repl.md
@@ -36,8 +36,7 @@ See `Pantograph/Protocol.lean` for a description of the parameters and return va
   - `{ "calc": <expr> }`: Execute one step of a `calc` tactic. Each step must
     be of the form `lhs op rhs`. An `lhs` of `_` indicates that it should be set
     to the previous `rhs`.
-  - `{ "conv": <bool> }`: Enter or exit conversion tactic mode. In the case of
-    exit, the goal id is ignored.
+  - `{ "conv": <bool> }`: Enter or exit conversion tactic mode.
   - `{ "draft": <expr> }`: Draft an expression with `sorry`s, turning them into goals. Coupling is not allowed.
   If the `goals` field does not exist, the tactic execution has failed. Read
   `messages` to find the reason.