There are Position Limits which are listed in the rules of the exchange where you are buying the option contract.
These are usually very high (e.g. of the order of 2.5 million contracts for Apple, Inc. at the time of writing per the OCC position limit data: https://www.theocc.com/webapps/position-limits )
There are also often limits on the size of orders that your broker or the exchange may accept through their system (so-called 'fat finger' checks).
Your broker may also be checking against the capital in your account to ensure that you have sufficient capital to be able to have the order executed. They don't want to run the risk of executing a customer order that the customer cannot pay for.
If you hold a certain number of contracts, you have the right to exercise those contracts - I am not aware of 'exercise limits' per se, unless you have insufficient capital to exercise them.
I would you suggest that you contact your broker to find out:
- What precisely is the limit that your are encountering;
- Whether that is an Exchange Rule, a FINRA rule, an SEC rule, or the Broker's own policy, and the rule number.
You can then look up the rule to get an understanding of what it is all about.