Explicit specializations are completely different classes that are separate from the primary template. You have to rewrite everything.
In normal situations where you control the primary template, you would typically have some sort of common base class or base class template to collect common structures.
With a given library, it is generally a very bad idea to add specializations (unless the library explicitly says it's OK). With the C++ standard library, this is outright undefined behaviour.
(The main problem is that other translation units may be using the template instantiation which you're specializing without seeing your specialization, which violates the one-definition rule.)