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?

<sup>YOU SOUND LIKE LIKE FUCKING CLUELESS MICROSOFT FANBOYS THE DAY AFTER MICROSOFT ANNOUNCED ITS OK TO CARE ABOUT TYPE SYSTEMS


FUCK OFF</sup>