diff --git a/test/types/aggregate.test.ts b/test/types/aggregate.test.ts
index b227a4099fd..0cf72c11339 100644
--- a/test/types/aggregate.test.ts
+++ b/test/types/aggregate.test.ts
@@ -1,4 +1,4 @@
-import { Schema, model, Document, Types } from 'mongoose';
+import { Schema, model, Document, Expression, PipelineStage, Types } from 'mongoose';
 import { expectType } from 'tsd';
 
 const schema: Schema = new Schema({ name: { type: 'String' } });
@@ -61,3 +61,41 @@ async function run() {
   expectType<ITest[]>(await Test.aggregate<ITest>().sort({ name: 'descending' }));
   expectType<ITest[]>(await Test.aggregate<ITest>().sort({ name: { $meta: 'textScore' } }));
 }
+
+function gh12017_1() {
+  const a: Expression = { $subtract: [
+    { $dayOfWeek: new Date() } as Expression.DayOfWeek, // errors
+    2
+  ] };
+}
+
+function gh12017_2() {
+  const a: Expression.Reduce = {
+    $reduce: {
+      input: '$values',
+      initialValue: { depth: -1 }, // errors
+      in: {
+        depth: '$$this.depth' // errors
+      }
+    }
+  };
+
+  const b: Expression.Reduce = {
+    $reduce: {
+      input: '$values',
+      initialValue: 0,
+      in: { $add: ['$$value', '$$this'] }
+    }
+  };
+
+  const c: PipelineStage.Set = {
+    $set: {
+      child: {
+        foo: 'bar' // errors
+      },
+      friend: new Types.ObjectId()
+    }
+  };
+
+  const d: Expression.ToInt = { $toInt: 2.5 };
+}
diff --git a/types/expressions.d.ts b/types/expressions.d.ts
index 8663e1a49fb..be5b5789741 100644
--- a/types/expressions.d.ts
+++ b/types/expressions.d.ts
@@ -1043,7 +1043,7 @@ declare module 'mongoose' {
        *
        * @see https://docs.mongodb.com/manual/reference/operator/aggregation/cond/#mongodb-expression-exp.-cond
        */
-      $cond: { if: BooleanExpression, then: AnyExpression, else: AnyExpression } | [BooleanExpression, AnyExpression, AnyExpression];
+      $cond: { if: BooleanExpression | ConditionalExpressionOperator, then: AnyExpression, else: AnyExpression } | [BooleanExpression, AnyExpression, AnyExpression];
     }
 
     export interface IfNull {
@@ -1957,7 +1957,7 @@ declare module 'mongoose' {
        * @version 5.0
        * @see https://docs.mongodb.com/manual/reference/operator/aggregation/addToSet/#mongodb-expression-exp.-addToSet
        */
-      $addToSet: ArrayExpression;
+      $addToSet: Expression | Record<string, Expression>;
     }
 
     export interface Avg {
@@ -2406,7 +2406,8 @@ declare module 'mongoose' {
     TypeExpressionOperator |
     AccumulatorOperator |
     VariableExpressionOperator |
-    WindowOperator;
+    WindowOperator |
+    any;
 
   export type NullExpression = null;
 
@@ -2478,7 +2479,8 @@ declare module 'mongoose' {
     DataSizeOperatorReturningNumber |
     CustomAggregationExpressionOperatorReturningAny |
     TypeExpressionOperatorReturningNumber |
-    DateExpression;
+    DateExpression |
+    DateExpressionOperatorReturningNumber;
 
   export type ObjectExpression =
     Path |
diff --git a/types/pipelinestage.d.ts b/types/pipelinestage.d.ts
index 4972d265de3..a9dfb4659e8 100644
--- a/types/pipelinestage.d.ts
+++ b/types/pipelinestage.d.ts
@@ -212,7 +212,7 @@ declare module 'mongoose' {
 
     export interface Set {
       /** [`$set` reference](https://docs.mongodb.com/manual/reference/operator/aggregation/set/) */
-      $set: Record<string, AnyExpression>
+      $set: Record<string, AnyExpression | any>
     }
 
     export interface SetWindowFields {