Here is the deal as I see it. The only players not on our books for next year are beasley and walker. Let's assume for argument's sake that if we don't keep them, we would fill their spots with someone who makes at least as much as they do.

Right now we are 11 million over the cap but 2 million under the tax. the tax line will go up by like 4 million next year. If we sign dragic, at say 18.5 million per year, that would be an 11m increase, putting us $5m into the tax. at that point we could only sign our mid level exception, and minimum contracts, and they would all come with more taxes.

In 2016, let's say we want to pay whiteside an increase of 19m per year. We don't know if the cap is going to be raised slowly or in one huge chunk. If its one huge chunk, like the players want, we could probably sign whiteside no problem. If it's a gradual increase, we would need to shed salary. Lets say the cap goes from 66 million to 74 million, double the jump next year. We would have to shed 30 million in salary in order to sign whiteside. Remember, we are currently at 75M, Dragic is going up 11M, and whiteside is going up 19M, for a total of 105M on a 74M cap, which you can't exceed to sign whiteside. Ennis, Napier, McRoberts, Bosh, and Dragic would all be locked in. Birdman, Udonis, Chalmers, and Dragic II, and Deng add up to about 25M. Everyone else is either guaranteed or already on a minimum. So, about 5M too much salary. So, here is what would have to happen, assuming we give up chalmers, birdman, deng, UD, and Dragic II. If the 2016 cap is 80M or higher, we are good. If wade takes 10M, we are good. Or, we could use a loophole where we only sign dragic to a 1 year deal next year, at 14M or lower, and then sign him over the cap using his bird rights the following year. (his 2015 salary would create a cap hold for 2016 so it would be necessary for him to take less.
So, TLDR, yes we can re-sign whiteside in 2016, but it will take maneuvering I am sure we can pull off.