RealGM

Can they sign another player even if they don't have the cap space/MLE/LLE/Vet Min and pay luxury tax?

Just curious.

A team can always use the vet min or the min to sign a player regardless if they're over cap

say for example... elton brand signs with celtics for max.... is that allowed?
as in we can pay him as long as we pay luxury tax. is this correct/allowed?

No we can't sign Elton, he'd be sick next to KG thou...we'd have to be enough under the cap like the 76'ers or Warriors to make an offer greater than the MLE/LLE/MIN

You should play a NBA game for a gaming console, it really helped me understand the caps.

This will answer your question. http://members.cox.net/lmcoon/salarycap.htm

Read the link already provided.

But the core idea is that a team that's over the salary cap (which is most of them, certainly including the Celtics) can not add a player except by using one of the specific provisions -- many of which are called "exceptions" -- in the CBA (Collective Bargaining Agreement). Key ways to sign a player are:

1. Larry Bird Exception, for players who haven't been a FA for three seasons.
2. Early Bird Exception, for players who haven't been a FA for two seasons.
3. Mid-Level Exception.
4. Low-Level Exception.
5. The exception that lets you resign any player to 120% of his prior salary or less, even if he hasn't been around long enough for Bird or Early Bird Rights. (It seems that the Cs offered this one to Posey, as many of hoped and/or predicted they would.)
6. The exception that lets you sign anybody to a vet minimum contract.
7. The right to sign players that you draft.

There also is an exception that lets you acquire players through trades if the salary coming in is not too much more than the salary going out.