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Discovering new types of feedback is the sound guy’s No 1 job. It takes precedence over all other jobs even turd polishing and creating tripping hazards for performers and audience members.
But seriously….

Assuming the mics aren’t in front of the speakers……… (If they are you’re boned- re install the system correctly)

If you have an RTA use it to help you find the problem frequencies.

If you don’t try this:

High pass the mics at 75.

Start by creating two notches of 9 db. One at 350 w/ a Q of 7, one at 530 same Q.
Sweep them up and down until you located the problems.

Also compress them at 3.5 to 1 with 3 db makeup gain. Set the threshold so it knocks the tops off the more energetic speech.

The surest way to windup with nothing is to wait for everything. On the other hand, the 2nd mouse always gets the cheese.