I had been mulling this over for a while, ever since jojokeo's post about why he wasn't getting more volume/power when switching tubes.
The only way to get the idea across is to create a post showing how much power small and big tubes actually make, if you keep things the same, as well as how supply voltage, available current and load impedance factor in.
If you want more volume/headroom now, add more speakers (or more efficient speakers). Aside from that, for the output stage to make more power, everything needs to be upped to make a bigger power stage/amp.
For an (over-)simple example, you want more power, so you use bigger tubes. The bigger tubes could pass more current, but the old higher load impedance limits the current swing. You swap OT (or load impedance) to allow the tubes to swing more current, but now you run into the limited current available from your existing power transformer and B+ supply. So you tack on another power transformer, maybe to raise B+ voltage as well as available current (because more supply voltage yields more possible voltage swing; increasing current swing and increasing voltage swing works on the power equation from all sides). Your bigger output stage may require more bias to tame idle current at the higher supply voltage, so now it also requires a bigger driving signal to push the output stage to its full capability; maybe you need an alteration to the phase inverter, or a new inverter circuit. Now that your revised power amp makes more power, are your existing speakers up to the task?
The point of the example is that an incremental change may not get the result you want.