Let's say we have a character with this build: Cleric 1/Druid 1/Warlock 1/Wizard X, and it has a Mizzium Apparatus.
Mizzium Apparatus reads (emphasis mine):
You can attempt to cast a spell that you do not know or have prepared. The spell you choose must be on your class's spell list and of a level for which you have a spell slot, and you must provide the spell's components.
You expend a spell slot to cast the spell as normal, but before resolving it you must make an Intelligence (Arcana) check. The DC is 10 + twice the level of the spell slot you expend to cast the spell.
On a successful check, you cast the spell as normal, using your spell save DC and spellcasting ability modifier.
Our character uses the Mizzium Apparatus to cast a Druid spell they did not prepare. Since they have multiple spellcasting abilities, which one is used to determine the spell save DC and attack roll modifier? Is it determined by the spell list to which the spell belongs, or is it the player's choice? What about spells that appear on multiple spell lists, such as Cure Wounds?
Best Answer
Use the spellcasting ability of the class with which you cast the spell.
The rules for spellcasting in case of characters with more than one class states (emphasis mine):
Per description, Mizzium Apparatus allows the caster to access to all spells in all their spell lists. This is equivalent, for example, for a Wizard to have all the spells that they can cast in their spellbook, as they know them. Since for divine casters the spells are always known, this magic item allows to try the casting of an unprepared spell.
The multiclassing rules are hence straightforward to apply. If you cast a spell from the Druid list, you must use the spellcasting ability of the Druid, if you cast a spell belonging to the Wizard's list you must use the INT ability and so on. In case you cast a spell that belongs to more than one list, you choose from which list (and hence the ability to use) you are selecting the spell.
A further motivation for using the multiclass rules for spellcasting relies on the item description:
which means that you are not casting the spell through the item\$^\dagger\$, but you are spending one of your slots. This means that you can upcast a Cure Wounds, for example.
Let's consider some cases for clarification.
\$^\dagger\$ A spell cast in this way can not be considered hence to be more than one class' spell at the same time, because it is not cast via the magic item.