Sorry, but no. Since you did not say, I'm going to assume equity options vs options on futures. After you do a trade and it clears, the OCC is your counter-party, not the other trader that took the other side of the trade. And, all the options at your clearing firm are lumped together at the OCC. The size of your trade makes no difference.
Short ITM calls options are only exercised early if the owner perceives more value in the long stock than the long calls. Some reasons might be:
-Large dividend that exceeds the value of the put on the same strike
-Very hard to borrow stock
-corporate event like a dutch tender offer
Then the OCC has a system for determining how many of each exercised call goes to each clearing firm and the clearing firms have a system for determining how that gets allocated to each account with short calls.