Absolutely. Remember two things:
1. The input voltage must be at least 3 volts higher than the regulated output voltage you want, so just make sure your source adapter is high enough. For 15V output, you'll want at least 18V input.
2. The more voltage you drop in the regulator, the hotter it gets, so bear that in mind for multiple outputs. With 18V input, and outputs at 15V and 9V, the 7809 will get hotter than the 7815. Possibly hot enough to burn you and/or cause thermal shutdown. Heat sink your regulators appropriately.
Happy New Year!