What a tantalizing question! A simple equation might aid to direct our thinking. Here is an equation for power of the engine--
Power = k*Pme*V*rpm/60
where k is "mechanical efficiency"
Pme is mean effective pressure
V is engine displaced volume per rotation
rpm/60 is the number of power strokes per second for a two-stroke engine, otherwise divide this by two for a four-stroke engine.
So there we have determined power by four parameters. Oh, and the strokes per cycle is a fifth. If you mean to hold ALL of these parameters constant, then the equation would say you can't increase the power. Of course, any one of the parameters could be increased to increase power. Hmm--the answer I like is, you can greatly increase power by switching to a two-stroke operation, holding all other parameters constant.
The suggestion was made that changing fuel can allow the engine to produce more power. Excellent! An index of the amount of power is the quantity of energy that can be added at stoichiometric conditions. Many elements are involved, including the temperatures of the fuel and air. A simple index (indicator) would be the low heat value times the stoichiometric fuel-to-air ratio.
This index for light diesel is 2931. The stoichiometric fuel-air ratio for dimethyl ether is 0.11 and the low heat value is 28870 kJ/kg. Then the index for dimethyl ether (a high cetane fuel) is 3176. From this, we see that dimethyl ether will produce about 8% more power than light diesel fuel. By the way, other factors, such as dimethyl ether's greater fuel mass and cleaner burning should make the gain somewhat more than 8 percent.
You cannot change power without changing at least some parameter of the engine. I take it that you do not wish to change any engine design parameter.
In this case, add more fuel. This will get you more power.
The engine may smoke excessively, may not hold up mechanically, may overheat, its reliability and longevity may be decreased, the connected devices - transmissions, shafts, etc. - may not hold up mechanically. Who cares, right? You want more power, you will get more power.
I didn't explain things very well in that answer. Let's try again. The equation for engine power is--
Power = k*Pme*V*rpm/(30*n)
where k is "mechanical efficiency"
Pme is mean effective pressure
V is engine displaced volume per rotation
rpm is speed in revolutions per minute, and
n is the number of strokes per power stroke. (There are two strokes per revolution.) For a two-stroke engine, n=2. For a four-stroke engine, n=4. So, n is the fifth parameter that determines power. Combining my two previous responses, and in support of your view, if we assume that the first four parameters are the ones to be fixed, then power can be increased by either changing to a two-stroke or by changing to a fuel that can supply more energy (such as dimethyl ether, or UDMH maybe!)