Is it possible to make an abstract method's parameter list have overridable length and types?

Absolutely not - that would break half the point of having the abstract method in the first place - no-one would be able to call it, because they wouldn't know which method signature had actually been written. The whole point of an abstract class is that a client can have a reference of type BaseClass without caring about what the type of the actual implementation is.

No, this isn't possible. An overriding method needs to match the parameters exactly—it's the same as implementing an interface. You may be interested in the double-dispatch pattern.

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