Theoretically you can do both. Practically, few languages give you the tools you'd want to ensure functional purity.

C++ is a multi-paradigm language, for instance. But it doesn't have any concept of immutable data. The 'const' keyword exists but it only does a very shallow check for immutability (i.e., the pointer won't change but its data might). And even with a 'const', there are still huge backdoors (the 'mutable' keyword).

Point being, it's possible, but you'd be relying on convention in your design and care in your implementation to make it work.