convert a 12VDC, 800ma wall wart to 22-24VDC, ~400ma

Or, change the rectifier system:
If it's half-wave: change to bridge, change the cap to correct voltage.
If it's bridge: change to voltage doubler, add second cap.

The above assumes it's an unregulated supply.
Voltage doubler circuits have poorer regulation, which may be an issue.

It's easier to go and buy a new one, but you can learn nore by trying:)