I think a better question would be if/how you could run a gym, but if/how you could run the program at that gym.
Were I running the team program at a gym, there would be little to no emphasis places on competition and scores. Our primary goal, and I would make sure every coach agreed with this, is to have fun and make the kids better gymnasts. As a coach, I find that, with surprising frequency, the goal of getting better scores and making the kids better gymnasts come in direct conflict with each other. Were I head coach, my instructions to other coaches when they run up against something like that would be to focus on making the kid a better gymnast, regardless of the effect on scores.
A perfect example of what I'm talking about is girls' level 4 vault. A handstand flatback on a mat. If I want to very easily teach my girls a zero-deduction body shape on preflight, all I need to do is scoot the board really far away from the mat and have the mat surface low, forcing them to stretch out their bodies to reach the distance. However, this does not teach heal drive, hinders ability to get a proper block, and forces the kids to completely re-learn vault when they take it to the table. This being the case, I say to hell with their scores, and teach them to vault with the springboard close and the mats stacked high. They most likely would score lower as a result of this, but they'd learn proper chest position on the board, proper heel drive, and they'd have a much easier time transfering to the table when the time comes. Thus, I sacrifice their scores to make them better gymnasts.