If the drawings/specs call for a specific part number, and they don't say "or equal", I usually don't approve anything else. Then again, that's because I'm typically dealing with airport authorities who have very strict standards that they paid somebody a lot of money to come up with. They're liable to make the Electrician rip it out and "correct" it, even if I did approve it.
You might be able to submit a substitution request, although some engineers charge for that so it might be cost-prohibitive.
All that being said, I've never given a specific manufacturer/model number for something like box supports. That seems like something the Electrician ought to be able to decide upon based on field conditions.
It really all comes down to who the engineer and the customer are, and what sort of relationship you have with them. I'm much more likely to give leeway (as far as I'm allowed by the customer) to an Electrician I've worked with before and had good experiences with, than somebody new.