It may cost you more money to not work for your client's competitors. I say that because it sounds to me like this client is a bread and butter client and may have dominance of your time? If I am wrong then just understand what I am saying is only a suggestion. Working for his competitors keeps you in business. That is something that ultimately your client doesn't worry about, i.e., keeping you in business. If it ever comes a time that he is no longer able to pay for your services, you may find yourself without work. So unless he is able to pay you enough to make up for that loss then why should he stand in the way of you taking on other competitors?