319 to 380
The older generation Airbuses seem to have a lot more common than the 380.
Quite a few airlines will give a CCQ (Cross Crew Qualification) to pilots who operate multiple Airbus types within a company.
Even within a single Airbus type, eg A330, there may be several different types or varients/series 200/300 etc and even within each of those there may be other differences too.....engines/software/weight limits etc.....so sometimes, even when flying "one type" you have a ton of numbers & different procedures in your head!
Cathay for example have the A330-300, A340-300 and until a few years ago, the A340-600....and some pilots would be qualified to fly all 3 types and the 340-600 was quite different to handle compared to the others. Just means you need to keep in the books more!! Once you're up in the front end, you just put your "other hat" on and away you go.....sometimes slowly and cautiously, depending on your recency.
Even though previous Airbus experience will allow you to zip through an A380 conversion, as there are a heap of similarities with older generation Airbus aircraft, personally, if you were on the 380, I think that you'd just want to focus on that one type. Although it has the typical "Airbus" layed out cockpit, the software/displays/FMS/systems have "some" similarities, but they are a fair bit different.....and being a long haul aircraft (limited sectors each month), you may run into recency issues with keeping qualified on other types.
The A380 aircraft systems are a lot more complex than your regular Airbus, and there's a miriad of things that can potentially go wrong or fail, so from the perspective of being on top of your "emergency handling game of what if....", it helps to be able to focus on just one type. That being said, a lot of emergency procedures are almost identical from one Airbus to the other, but.....there are some significant differences between handling some types of emergencies on an A319/320/321 compared to an A380.
So, yes you can be qualified on several different types of Airbus jets, and it does happen, but there are common sense limits applied in most cases so that safety doesn't become an issue.
The good thing about Airbus aircraft is that everything is almost in the same spot in the cockpit for the most part, your hands and feet know where to go!