The key to private student loan consolidation is getting your payments into one single monthly outflow. Even though the government itself will not consolidate your student loan, many private financial institutions will step into the void. This is due to an implicit guarantee from the government that it will insure these private lenders for any losses you might cause during a student loan default.
The good news is that because, in most cases, your consolidated private student loan will be based upon your current credit score, not the score that was the basis for the original student loans. That means that if your score has improved substantially, your combined payments may be lower than paying each loan individually.