Is double-lugging permitted on class 320 meter bases, or do they have dual lugs for parallel service conductors?

When you say "doubling lugging", do you mean two wires under one lug?

This is OK ONLY if the lug is rated for two wires, and yes there are lugs with multiple ports for more wires per leg.

Check with the manufacturer of the meter for accessories or options availalble for the different lugs.

Most times, lugs do not come with 320 amp meters, and must be requested for the quantity and size of the wire being used, both for line and load.

I doubt a one port lug is available for two #2/0 wire, but there definitely is two port lugs that can bolt onto one stud. One port for each wire is much better, even if multiple wire rated lugs are available.