Hey guys! I recently bought a Alvarez 90’s model mandolin, and it’s amazing and I love it. However, when I play, the pick guard always buzzes. I tightened all the screws around it, but it still buzzes! I have no idea what else I can try to eradicate it. Any ideas or tips? They would be most appreciated 
Pick guard buzz
Buzzes are an adventure. Depending on the type of pickguard, it could be lots of places. If it is easy to do, I’d start by removing the guard to verify the buzz goes away. If it does, since you have already tightened it, maybe some tiny o-rings on the screw shafts would take care of it. I had a tailpiece cover that I couldn’t get to stop buzzing. It wasn’t needed, so I took it off and it has remained in the case pocket for over a decade. I don’t miss it a bit.
It’s weird in that it could sound like the pick guard, but not actually be it. Mike has a great suggestion with removal, but it wouldn’t surprise me if it’s something tailpiece related that seems to emanate from the guard.
Thanks for the help @Mike_R and @BanjoBen! I have taken the pickgaurd off and the little piece of felt that goes over the screw looks old and very thinly worn. Do you think I should get a new piece of felt to go over the screw so that the screw doesn’t hit the guard and make the buzz sound?
I also took the tailpiece cover off, and it still buzzed, so it wasn’t that! 
It could possibly be the knobs on the tuners. Sometimes they will come loose and a little tightening will fix them right up.
Take the pick-guard off, that was my first thought. 
Will the sound of the mando be different if I take the pickgaurd off?
If the sound is noticeably different, my guess is that it would be an improvement.
Is it buzz free without the guard? You asked about the felt… yeah, if that seems to be the issue new felt or something else in there would be good.