Variations of cloud types are created by combining the cloud's shape/description with the altitudinal names as a prefix or suffix.
Cirros (high) or Cirro can be used with cumulus (heap) to indicate a cirrocumulus or high, lumpy cloud. Cirrocumulus clouds, sometime called "mackerel skies", can indicate the approach of a hurricane in the tropics. It can also be used with stratus (flat, layered) as in cirrostratus to indicate a high, flat or layered cloud.
Alto can also be used with cumulusand stratus to indicate altocumulusand altostratus which are middle altitude lumpy clouds and middle altitude layered clouds respectively.
Nimbo or nimbus might be used with cumulus or stratus to indicate a cloud formation that is producing precipitation. These clouds could be either cumulonimbus which would be a lumpy, vertically-rising rain cloud or nimbostratus which would be a sheet or flat-looking rain cloud.