diff --git a/dojo-typings/src/main/typings/dijit/dijit.d.ts b/dojo-typings/src/main/typings/dijit/dijit.d.ts
--- a/dojo-typings/src/main/typings/dijit/dijit.d.ts
+++ b/dojo-typings/src/main/typings/dijit/dijit.d.ts
@@ -592,7 +592,7 @@ declare namespace dijit {
          * Set a property on a Stateful instance
          */
         set<K extends keyof this>(name: K, value: this[K], ...opts: unknown[]): this;
-        set(values: Partial<this>): this;
+        set<K extends keyof this>(values: {[k in K]?: this[k]}): this;
 
         /**
          * Watches a property for changes
diff --git a/dojo-typings/src/main/typings/dojo/store.d.ts b/dojo-typings/src/main/typings/dojo/store.d.ts
--- a/dojo-typings/src/main/typings/dojo/store.d.ts
+++ b/dojo-typings/src/main/typings/dojo/store.d.ts
@@ -48,7 +48,7 @@ declare namespace dojo {
 				matches(object: T): boolean;
 			}
 
-			type BaseQueryType = string | object | ((...params: any[]) => any);
+			type BaseQueryType = string | object | ((...params: unknown[]) => unknown);
 
 			interface QueryEngine<T extends object, Q extends BaseQueryType> {
 				<O extends QueryOptions>(query: Q, options?: O): QueryEngineFunction<T>;
@@ -209,12 +209,12 @@ declare namespace dojo {
 				/**
 				 * Stores an object
 				 */
-				put(object: T, directives?: PutDirectives<T>): any;
+				put(object: T, directives?: PutDirectives<T>): unknown;
 
 				/**
 				 * Creates an object, throws an error if the object already exists
 				 */
-				add(object: T, directives?: PutDirectives<T>): any;
+				add(object: T, directives?: PutDirectives<T>): unknown;
 
 				/**
 				 * Deletes an object by its identity
@@ -249,12 +249,12 @@ declare namespace dojo {
 				/**
 				 * Stores an object
 				 */
-				put(object: T, directives?: PutDirectives<T>): PromiseLike<any>;
+				put(object: T, directives?: PutDirectives<T>): PromiseLike<unknown>;
 
 				/**
 				 * Creates an object, throws an error if the object already exists
 				 */
-				add(object: T, directives?: PutDirectives<T>): PromiseLike<any>;
+				add(object: T, directives?: PutDirectives<T>): PromiseLike<unknown>;
 
 				/**
 				 * Deletes an object by its identity
@@ -297,12 +297,12 @@ declare namespace dojo {
 				/**
 				 * Stores an object
 				 */
-				put(object: T, directives?: PutDirectives<T>): any;
+				put(object: T, directives?: PutDirectives<T>): unknown;
 
 				/**
 				 * Creates an object, throws an error if the object already exists
 				 */
-				add(object: T, directives?: PutDirectives<T>): any;
+				add(object: T, directives?: PutDirectives<T>): unknown;
 
 				/**
 				 * Deletes an object by its identity
@@ -485,13 +485,13 @@ declare namespace dojo {
 			 * Stores an object. This will trigger a PUT request to the server
 			 * if the object has an id, otherwise it will trigger a POST request.
 			 */
-			put(object: T, options?: JsonRestPutDirectives<T>): PromiseLike<any>;
+			put(object: T, options?: JsonRestPutDirectives<T>): PromiseLike<unknown>;
 
 			/**
 			 * Adds an object. This will trigger a PUT request to the server
 			 * if the object has an id, otherwise it will trigger a POST request.
 			 */
-			add(object: T, options?: JsonRestPutDirectives<T>): PromiseLike<any>;
+			add(object: T, options?: JsonRestPutDirectives<T>): PromiseLike<unknown>;
 
 			/**
 			 * Deletes an object by its identity. This will trigger a DELETE request to the server.