Sounds like it's not getting enough light.

tndaisy, you certainly can prune your gardenia to improve its form, and doing so right after it's finished blooming is the correct timing.

Take on this task with a pair of sharp secateures or loppers and take some time with it so that you can avoid a square or round eyesore instead of a more pleasing natural form.

Prune to an outward growing branch, stem, or bud. Your plant will automatically respond by sending chemical/hormonal signals to dormant vegetative buds further back on that stem, forcing them to activate and make more leaves and branches.

Hopefully, your gardenia receives three or four hours of morning sun. I happen to think that protection from the afternoon sun is ideal for gardenias, but they do need plenty of direct sun in order to be at their best.

Thank you both! It gets the 3-4 hours of morning/mid-day sun, and seems to be very happy- it is laden with blooms- the weight of which I suspect is part of the problem. Will prune when blooming is over, hoping to root cuttings...Linda

This was (I moved away from it) in the sun from about 8-9 AM until sunset. Already there when I moved into that house. I trimmed it occasionally because we needed to be able to walk around it, but there was never any leaning.

This is a cutting from the above shrub, in the sun from sunup until about 3 PM. Pic from a couple weeks ago.

I put a few cuttings from it in my Mom's yard (a couple yrs before the above) and they are not as upright, more distant nodes, not as many blooms.