It depends on the specific model.
For example the 2006 Suzuki DF9.9 4 stroke can be upgraded to a DF15 by replacing the carburettor. The 2009 DF9.9 is actually a beefed up DF8, so cannot be upgraded.
If there is a Johnson 15HP that has the same vital statistics as the 9.9 (ie bore, stroke, compression ratio, gearing, weight, etc) it might be possible.
You need to compare the parts lists. If the only difference is for example the carb, it may be possible if you can do it cheaply enough. If it is the camshaft, ignition system or a number of other things it is likely not worth the hassle.
First step may be to see how much you can trade your 9.9 in for against a 15.