Argument Subclassing, static_cast

Let's say I have a class Foo with a virtual method

virtual void initialize(InitParams& params);

Since there will be classes that derive from Foo, is it good practice to also subclass InitParams and static_cast them to the specific InitParams for that class?

Me as a programmer has to ensure that I actually pass the correct InitParams to the method. Are there any other downsides? I want to store multiple Foo instances in a collection so it's important for me to have this generic virtual initialize method.