Write generic multi-dimensional Map type

Question

I'd like to create a generic multi-dimensional map type where the last of N types is the final value and the preceding types will effectively be a key.

In other words:

let m:MDMap<Coat,Pie,Date,Location>;

//...

m.get(myWoolCoat,myApplePie,yesterday) // returns a Location

Without variadic generics though it looks like I'm going to end up with something like this:

export type MultiMap<
    A extends any,
    B extends any,
    C = void,
    D = void,
    // ... etc.
> = D extends void 
      ? C extends void 
          ? Map<A,B>
          : Map<A,Map<B,C>>
      : Map<A,Map<B,Map<C,D>>>

let m:MultiMap<Coat,Pie,Date,Location>;
    

I know Typescript handles variadic tuple types but I haven't been able to bridge that ability to something resembling the above desire.

Should I make do with the work-around or is there some way to pull off some kind recursive generic?