In most cases, yes you can refinance your student loans after consolidation.
If you previously refinanced your student loans through a private lender, you can refinance again with or without including any eligible new loans. It is advisable to go through the entire process again, from comparing lenders, to choosing a lender and applying. This will help ensure you get the interest rate and terms that are right for you.
You may also refinance a Direct Consolidation Loan through a private lender as well.
If you want to consolidate your loans again through the Direct Consolidation Loan program, you will likely need to include a new eligible loan, which was not part of the original consolidation. Check with StudentLoans.gov to learn more.