Is there an AR or something similar that puts a cap on how many Specialists or Corporals an Aviation Company may have at once?

Modification Table of Organization and Equipment (MTO&E). Youbcan download it from FMSWeb if you have access. Your unit supply should have access. You'll need your UIC to download the one specific to your unit. Below was pulled from AR 71-32.

A TOE is a requirements document that prescribes the capabilities, organizational structure, and the minimum mission
essential wartime requirements (both personnel and equipment) necessary for a military unit to accomplish its doctrinal
mission and the capabilities required by the unit to perform its core functions and assigned universal tasks to fulfill its
designed purpose. It is the basis for an authorization document, the MTOE. The TOE numbering system is described
on FMSWeb. All TOE conform to a standard format. TOE are initiated when TRADOC provides an approved
requirement determination packet called a FDU to DCS, G–3/5/7 (DAMO–FMZ). USAFMSA builds TOE for different
types of organizations, and then they are considered for authorization by quantity and by component during TAA.

It depends on the MTOEof the unit. When you look at the MTOEit will show you how many of each rank, what MOS they are, and even down to the equipment that is assigned to that unit or section. The MTOE is going to differ from Brigade, Battalion, and Company. In some some rare situations Soldiers can be double-slotted in a billet. If you are really interested you should be able to talk to your Platoon Sergeant, Platoon Leader, or 1SG.

It's called FMS web. Google it. You can search by UICs and see the breakdown of the authorization for personel, equipment, etc. This is pretty standard for company command teams to have. This is something that officers and NCOs with the know-how to look and see what's required of their organization. This is what the Army dictates.