Can I mix & match different tires?

[Luisito]

Before I begin, I'm pretty sure someone has already asked a similar question as this. I looked but didn't see any, so I decided to make this thread. My apologies if I am being redundant.

Hello, my 2006 X5, E53 4.8is needs new tires. A co worker gave me two tires that his son took off of a different car with about 100 miles on them, so they are relatively new. They are Pirelli P Zero Nero All Season in a 275/40R20 so they would fit in the front. I went online and looked for that same tire in a size 315/35R20 for the rear but Pirelli doesn't make that tire in that size. It looks like I have to get different tires in the rear.

In my research I have found that everyone says we cannot mix and match tires on all wheel drive vehicles but the X5 comes from the factory with different sizes on the front than the rear. How is this possible if they are supposed to be the same size?

I bought this X5 in November of 2020, used of course and it currently has Pirellis in the front and Continentals in the back. I could just buy the same tires for the back but I kinda wanted to keep all the tire brands the same.

Can someone help me understand why we are not supposed to mix and match, even thought they come off the assembly line with the staggered set up? Also any suggestions on what tires I could get for the rear?