There is a Smith & Wesson advertisement for the M&P .38 Special 2" revolver that states it can safely shoot two cartridges, the .38 Special and the 38-44 High Speed and it lists the velocity for this round at 1125 fps. and also states that company VP Major D.B Wesson has recommended these cartridges. This ad is obviously Pre-Model 10 so I would say you can safely shoot modern day +P cartridges.
Don't go by this.
The Great Depression was on, and sales were hard to come by. Both Smith & Wesson and they're principal competitor, the Colt Company sometimes went off the deep end when it came to advertising.
In this instance Colt opened the ball by claiming that the super-hot .38-44 loading of the .38 Special cartridge could be fired safely in any (then current) Colt .38, including the Detective Special.
This put Smith & Wesson in a bind because their position was that the .38-44 load should be used only in the .38 Heavy Duty (service) or .38 Outdoorsman (target) revolvers built using the large N-frame platform. Colt had previously only recommended using it in their Single Action Army and New Service/Shooting Master guns.
Smith & Wesson did a little experimenting and found that limited use of the hot load in a recently introduced 2" snubby version of their popular K-frame, .38 Military & Police model didn't blow the gun up, but the recoil was to say the very least - abusive.
Thus they speculated that in most cases the shooter would give up before the revolver did. In addition peek pressure was slightly less because of the ultra-short 2" barrel, that produced a massive muzzle flash indicating that the slow burning powder usually used in .38-44 ammunition was burning outside the muzzle where it was harmless. In the relatively few instances where a shooter actually fired enough of the ammunition to damage an individual revolver, causing it to suffer from progressive stress (rather then a KABOOM!) they would replace it.
Fortunately before long World War Two came along, and after the war it wasn't long before both companies dropped any mention of using .38-44 cartridges in anything but their most stout models.
I would add that shooting both Smith & Wesson's and Colt's smaller and medium frame, pre-war and made-during-the war revolvers with ammunition that
might generate extra-ordinary pressure isn't a good idea.
While the possibility/probability of inflecting damage may (or may not) be remote; If it does happen it will most likely be in the form of an expanded (not ruptured) chamber(s) that would require a new cylinder to fix, and neither of the above cited companies will touch it with a ten-foot pole.