You need to lower the voltage to the pass transistor, so you reduce its dissipation at low voltages (a linear power supply converts all of the excess voltage to heat). If you don't change the input voltage, the pass transistor will have to dissipate more, and will probably overheat. For the pass transistor, lower voltages require more dissipation than higher dissipation.
To lower the voltage input voltage to the pass transistor, you want to use only part of the secondary windings. In the case of a transformer with two secondaries for a total of say 30V, you would only use one winding (or both in parallel) for 15V output. The total rating is the total for all secondaries. If you only use half of them, you can only use half the power. You can draw somewhat more power when not loading one of the secondaries, but I wouldn't count on twice the power. The wire gauge in the secondary is designed for a certain current (eg. 200VA/30V), it will get hotter at twice the current).
When modifying an existing design, you may also have to replace the bridge rectifier and smoothing capacitors. You'll also have to tweak the current limiting circuit.
For switching power supplies, it's a completely different story, I wouldn't recommend doubling the current without a thorough review of the design.