There is a pre-made ship that has a listing Recreation Suite (HAC/Gym). Do the rules allow for a multi-purpose suite? Each of those(HAC and Gym) have different power demands, but same BP.
Lacking any guidance in the book beyond that they actually do have that combo room in one of the prebuilt ships, so it's clearly intended that you can combine them, I would say that you would just stack the PCU and BP costs of the different rooms but it only takes the one expansion slot.
While Fuzzypaws has mostly stated what I would say, I will note that if you're talking about the Sunrise Maiden in Dead Suns 1, there is implicitly no extra charge for throwing a gym in on top of a HAC. The Sunrise Maiden doesn't have any build points to spare if you reconstruct it with just the HAC, but it has the gym anyway. That, or it's a fudge or error that gives it an extra build point beyond what tier 3 ships can have.