data class <T> MyClass(...)

should work

I think you mean MyClass<T>, but wouldn't that mean that T would be the same class for every key/value pair in the map?

yes, that is true

In that map, I need to have <Key<Int>, Int> and <Key<String>, String> pairs

try using upper bounds

not sure what those are

I know, I looked there, but I think that would allow <Key<Int>, String> pairs

good point, I missed that one

I'll keep looking 🙂

cool, thanks for getting back with some answer