Okay, but there are several differences.

1. The bullet on the 9s is much lighter than that of the .45. About half the weight, means much less recoil impulse.

2. The chamber and barrel are the same external dimensions of the .45, so that means the walls are much thicker and will handle much higher pressures.

3. A useful comparison is the 1911 in .40. The .40 can be thought of as a type of .45 +P, since the bullet's only 50 grains different. There's a reason that Colt, Kimber et al dropped it not long after the introduction. It's too much mass and too much pressure for the 1911. Slide goes too fast and it can cause intractable problems. The design just won't handle it.

So the 1911 can handle 9mm +P and .38 super, but not (reliably) .40. I'd say the .45 +P is more like the .40 than it is the smaller calibers.

Again, I'd pass on .45 +P. You're asking Browning's gun to do something it wasn't designed to do.