Well theoretically there is nothing to stop CAC to come up with an alternative design. They probably need to consider 3 things 1) how much spare design capacity can be diverted from their main line, namely J20. 2) depending on 1), how likely can their proposal be vastly superior compared to FC31 in meeting the requirements. 3) what is the likelihood of their proposal being selected by the military and therefore having monopoly in the business, which would imply SAC and its army of sub contractors may run into difficulty or even go under when the work of 3-gen fighters starts drying up in the future.
On the other hand, there is in no hurry of making a rushed decision for PLAAF on the lightweight given FC31 and the CAC theoretical proposal will reply on the new engine that is being working on, which means there is still some time for SAC to fine tuning their work. Should SAC decides that they are in the position to come up with an new fighter, should they go after the top of the line fighter opportunity for Navy or go after the lightweight one for PLAAF? I think they will go big and design a new heavy fighter for Navy aviation.