No, there isn't. There are many factors involved in MTOW besides engine horsepower. So, unless you know whether the MTOW is limited by stall speed (max 61 knots for singles), structural strength (usually due to either gust, maneuvering, or landing loads), or performance (usually the balked landing minimum climb gradient), you can't tell if or how much the MTOW will increase if you increase engine power.
That said, there is a lot you can infer if you really look into the data. For example, we know that a 160 HP Cessna 172 obtains a 100 lb gross weight increase from 2300 to 2400 just by limiting flap travel to 30 degrees from the original 40 degrees. That suggests that the original MGW was driven by performance, specifically, the balked landing climb gradient (which is usually determined with flaps full down). Replacing the engine with a 180HP gets you another 150 lb if the flaps are so limited, which tells us that the 2400 lb limit was also performance-driven because there is no structural change with that engine change. Now, is that new 2550 lb MGW is limited by performance or by structure? If we look at the data on the 195HP Skyhawk XP (model R172K), we see the same 2550 MGW as the 180HP STC'd 172 (or the factory-stock 180 HP 172Q, of which there are few to be found) despite 15 more HP, which suggests the 2550 limit is driven by structural strength, because stall speed is still well below 61 knots.
Bottom line is there is no simple calculation -- you have to do a lot of research and analysis to even be able to guess what the potential increase in MTOW is possible given an increase in engine power.
