It's simple. Just be smarter than the manufacturer.
All you have to do is replace the amplifier chips with more powerful ones , on a bigger heat sink , and replace the power transformer with a larger one . The fuse, rectifier, and filter capacitors will get larger. This might not fit in the original case so you replace that too.
If the speaker was specially selected for this amplifier, you should replace it with a higher power rating. If it had a well designed cabinet which accounted for the T/S parameters, you'll need to modify or replace the cabinet.
What did you save? If you're lucky you can re-use the power cord and the knobs.