Can I have multiple classifications for the same fee schedule?

Yes, you can have multiple rates set up with different classifications in the same fee schedule. The time entry controls which fee schedule entry is used based on the matching combination found there and the Priority assigned to them. There is no way to assign classification to employees for projects, unless you use project assignments to do so. You can change the rate and classification at the time entry level also; however, BQE CORE does not remember it for the future.