What are next steps for a company that already has very high customer satisfaction scores?

Retain, hi level of customer satisfaction already scored.

Keep working on improving them even more. Your competitors are trying to catch you. If you sit back and wait, they may eventually catch you or surpass you. If you snooze, you lose.

Congratulations and keep it up. You could simply remain excellent what you do, or if you are in an industry where you can truly offer more products/services, you could try broadening out a bit. If you've really got satisfied customers, one of the best things to do is to ask them what they'd like to see you offer. Probably they'll tell you, but you could also offer some manner of incentive--some gift, discount, or a drawing even for responses.

If you don't already do it, it might be good to offer training opportunities--possibly partnering with a college or even high school.

You will also want to keep your employees because customer satisfaction is very much about the employees--how they treat customers, how the services are delivered, or goods made. So you can see if there are things you can do to make them want to stay and possibly even have more input into the company. Same as with customers: ask them.

See if people can figure out what makes you successful. Too many people have success then want to run an empire and everything gets ruined in the process. Don't grow beyond what you can continue to support in strength is the basic message.

Time to cross promote and optimize your customer database.