A magnum primer generally has a smidge of powdered aluminum added, which contributes fuel to the primer burn- hotter flame, longer duration- a bigger match to get the powder lit. Useful for hard to light powders, and in severe cold weather
When you change any ONE component of a load- powder, bullet, brass, primer- go BACK to the starting load. If the recipe calls for a standard primer with X grains of powder Y and bullet Z, that has been found to give safe pressures. Start going outside the recipe, and you may be damaging innocent bystanders.
WILL it give higher pressures? Maybe. Too many variables to give one answer. Here are SOME results with ONE rifle caliber:
Here is a short summary of the A-Square test of primers in the Remington 7mm Mag. as published in "Handloader" magazine.
160 grain Sierra boat-tail, 66.0 grains of Hodgdon H-4831 and Winchester cases.
Winchester WLRM (magnum) 3045 fps, 67,600 psi
Winchester WLR (standard) 3024 fps, 64,400 psi
Federal 215 (magnum) 3036 fps, 61,400 psi
CCI 250 (magnum) 3039 fps, 61,500 psi
Remington 9½ M (magnum) 3041 fps, 59,300 psi
CCI 200 (standard) 3011 fps, 54,800 psi
What we have here is... failure- to communicate.