Thanks for chiming in. Does this extend to forum accounts that are associated with those customer accounts?
The OP's question ties into this, even though it's not specifically a 1:1 customer account to forum account.
I don't want to beat this topic to death, so I'll just summarize my thoughts and you can consider it (or not). That there are lots of real, meaningful reasons to have multiple forum accounts, and doubly so in an environment where you're often getting professionals who are seeking information to support a business of whatever size, whether it's $20/month or $20/hour. Sometimes that's posting under a specific business account, sometimes it might be posting under a personal account to protect the privacy of the business.
If there's a behavior that's intended to be curbed by curtailing multiple forum accounts, it might be better to clarify a rule about that behavior, rather than impeding your customers' ability to maintain privacy or separation in their business relationships. Using discretion in banning as Brogan indicated in the other thread, or a wink-wink "it's okay as long as it's legit" policy, doesn't help the fact that most people will believe it's not okay to do it at all.