Mixed tyre brand type question

[shadow85]

Current setup:
245/40R19 (F) Pilot Super Sport
275/35R19 (R) Pilot Super Sport

I bought new Pilot Super Sports last year for my Z which only recently got boosted. It turns out I am going to need something alot more grippy on the rears because I am easily spinning out of control with these tyres.

So I have decided I will get a set of new tyres, perhaps some semi slicks like either of:
PROXES R888R or
POTENZA RE71R

But instead of blowing money on a whole new set of tyres, is it permissible to change out only the rear tyres from the Pilot Super Sports to either of those 2 semi-slicks mentioned above and keep the front as it is already, or is it a must to change out all 4 tyres?

Looking to go wider on the rears if possible aswell.