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Since in the fluff several SM armies may work together, will it be looked down upon to create an SM [TT] army that comprises of members from several chapters? For example, to create an army with Ultramarine sternguard, Imperial Fist tacs/devastator, and black assault marines (Ravanguard)?

What you're doing has been called by some as "Rainbow" marines.

I wouldn't have a problem with it. Have you considered a large Death Watch deployment?

It's fine.
Lots of examples in fluff for it.
Doesn't even need to be Deathwatch (Though that'd be really cool)

as long as they're all Codex Marines.

So ultramarine tac squads, imp fist devs, White scars bikers, Ravenguard assault marines and blood ravens Librarians could form a Legal tabletop army.

Now playing Codex marines with a squad of Long fangs included would be illegal.

Or all Blood Angel successors with the Blood Angel codex. You get the point

As long as you aren't mixing rulebooks, what color your paint your Marines and what you call them is kind of irrelevant. Certain combinations might not make sense from a fluff standpoint, but it's a tabletop game, not a story that you're writing.

If you are just painting each unit as a different chapter, go for it, call it a crusade force of space marines, each unit added to the cause from a different chapter.