Is there any sigma beyond six sigma?

In theory, there are infinite sigmas beyond six sigma. In reality, the cost and ability to move from six to seven sigma in a business process is usually not worth the return. At a six sigma quality level, you would expect 3.4 defects per million. At seven sigma quality, you would have 0.007 defects per million.

There are some processes that may run at seven sigma quality, but six sigma is a better goal which the vast majorities of businesses will never manage to reach.