Can a design framework be created upon another?

Is it correct, can, or should I base my design framework on another, eg. material.io?

I've been researching this but I can't seem to find a answer to back one of the opinions. Help needed!

Context: I'm creating a new framework from scratch, to represent my company's language and brand. I believe I should make it depend as little as possible from another packages, to make it more stable, easier to upgrade and also have less code. However, a colleague believes we shouldn't reinvent the wheel and so we should build our own upon, for example, vuematerial.io. More context: founders and engineering manager already agreed they want their own design framework, so resources/time isn't an issue.