Hi teen, the CAA (and pretty much every other aviation regulator out there) rule is that a crew member can not be trained on more than 3 aircraft types. That is to say, that crew cannot be trained on more than 3 different types of doors and if the aircraft doors are alike, the aircraft has to be similiar too.
SO, A crew member can be trained on the A319/320/321 and this would be counted as one aircraft.
In BA our LHR fleet is split on two...Eurofleet which consists all the Airbus aircraft, the B757 and the B767. All EF crew are trained for these aircraft.
The other fleet...worldwide consists of the B767, 777 and 747. This too is three aircraft and therefore the crew can be trained for all three, however only about half of the crew are as the B767 longhaul fleet is pretty small so this does leave a large number of crew capable of being trained on something else...hehehehe, doubt they would like that some how!!!
Virgin are technically trained only on TWO aircraft as the A340-300 has the same doors as the A340-600 but obviously the crew themselves would treat the two as different aircraft, but regards licence rating I dont think it is!
Hope that answers your questions!