I can't see a reason why this hurts, but it's probably not worth it. The only benefit I can see it having is if the user reuses their passwords on other sites, as now a potential malicious MITM would have to brute force the client side hashed password in order to reuse it on other sites. They would still be able to use that client side hashed PW to authenticate to the service in question, though.
Basically, hashing on the client does absolutely nothing for the security of the transfer or storage of the password. Whatever the client passes to the server, whether it's hashed or not, is effectively their password, and intercepting that (again, whether hashed or not) would give an attacker the actual credentials of the user.
There is zero downside to doing an extra hash, except the chance that someone codes such a basic thing wrong.
But only if neither site uses salt, so salt all your hashes. (Not even a salt is necessary here, just a site-wide addition would be fine. Or honestly you could just use a hash that wouldn't be used by a site too dumb to salt their database.)