Static AND Dynamic Typing?

Is it possible to create a language where it's statically typed (preferably with inference) by default, but can drop to dynamic typing for bits where you need it. I seem to remember someone saying this wouldn't work. Can anyone explain why?

This would work. In Haskell you can have values of type Dynamic. However, you have to unwrap them explicitly (conceptually not unlike unboxing in C#, or dynamic_cast<> in C++) and catch the cases when the contents are not of the type you expected.

Generally type inference is about as good, except for heterogenous collections. But I think there's a Haskell library for those, too, and for simple collections (i.e. ones that don't operate on the "leaves" of the structure) you can just use Dynamic or define a datatype with as many distinct leaves as you have types.

In the end, good design tends to make dynamic typing unnecessary. Unify your data model at a higher level, and refactor to fit.