MySQL does not (currently) support non-Key columns. For other DMBS you will need to check the reference manual.
A similar question has been asked and answered here. However since the performance improvement gained by using covering indexes is generally greater for non-selective queries returning a large number of rows, I can't envisage the solution of just including the extra columns within the index itself ever offering a performance improvement. However, there may be scenarios I am not thinking of, and yours may be one of these, so as always when looking for performance improvement, testing, execution plans and IO statistics will tell you far more than my conjecture!