Yes, you can add the new insulation on top of old insulation, unless it is wet. If it is wet or appears that the insulation has previously been wet, you should look for the cause and repair the problem to prevent a reoccurrence. Remove any wet insulation. Wet insulation can lead to mold, mildew, or even the rotting of your ceiling or roof rafters.
1) Do not place "faced" insulation on top of existing insulation in the attic. Any new batt or roll insulation added on top of existing insulation in the attic needs to be without a vapor retarder (face). Most vapor retarders on fiberglass are made of kraft paper. The presence of this paper vapor retarder on top of between layers of insulation can trap moisture leading to mold or even rotting. Any existing batt or roll insulation in the attic should have the facing against the attic drywall floor or no facing at all.
2) Either batt or rolled insulation or blown loose-fill insulation (fiberglass or cellulose) can be installed on top of old insulation.
3) If your new insulation is rolled insulation, you should roll it out perpendicular to the joists. Be sure to use un-faced rolls. If you cannot find unfaced rolls, you can simply pull the kraft paper (vapor retarder) off without much loss of insulation. You should not tack down rolled insulation. Insulation need to be fluffy to block heat flow. You will reduce the R-value of the insulation by squashing it flat to tack it down.
4) If you discover vermiculite insulation in your attic, be sure to have it tested for before doing work there. If the test reveals that asbestos is present, the vermiculite should be removed by a certified removal expert before disturbing it with the installation of more insulation.
5) Alternatively, you can also hire a local contractor to blow loosefill insulation (fiberglass or cellulose) in your attic. The process takes a couple of hours.
Visit the Insulation Fact Sheet for more information.
EPA highly recommends air sealing before adding more insulation.