Needed tire-pressure is all about actual load on tire and maximum speed you use and wont go over for even a minute, and a bit about alighnment specific the camber angle above 2 degr wich is sometimes done behind on sportif cars.
I once got hold of the formula the European Tire- and Car- makers use to determine the advice pressure and went running with it, and in time even constructed my own and learned a lot about it.
Now if you have other tires then original and maximum load and or Loadrange is different ( other loadindex and or for instance XL instead of standard load P-tire), then the advice pressures also need to be re-calculated.
If you have aftermarket tires of same sises and Loadrange , though the brand or model is different , then in general you can use the same advice pressures.
For instance you have a 195/65R15 91T tire ( wich I had of European system)for brand A, and you swich to brand B and tire sise and Loadrange stay the same, then maximum load also stays LI 91= 615kg and AT-pressure stays 36psi/2.5 bar.
If I would swich to 195/65R15 95T XL(=reinforced/Extraload)= 690 kg maxload AT 42psi, and those values are filled in the formula and it would lead to a bit higher advice pressure for the same load.
American AT pressures are a bit different, Standard load always 35 psi/2.4 bar and XL/Extraload/Reinforced 41 psi/ 2.8 bar.