How deep do you let the run ITM. So you faded the FED after the last cut. Your put protection is working out great. You made the right call. How greedy do you get? You know in the back of your head the market will rebound on something we can't predict like the 3rd week of August on emergency FED cut. When do you cash in? On a gap down Monday? Let it ride till Friday? You buy Dec. calls?
Cannot answer a question in general. For me I would need to know what strikes and what purchase price and what is current price. If it went really far ITM I could certainly make adjustments such as selling puts to roll into bear put spread and take initial debit and a lot of profit off the table and let the spread run. I could close the put and use a portion of the profits to buy more ATM or slightly OTM puts in case it continued to run lower, if not I banked profits already. I could add some calls to convert to ITM strangle with locked in minimum profit but still keep room to run. Lots of possible adjusments but for me it would depend on how much profit I have so far and where my strike is.