Just a quick question from a rather new player; tried looking up the answer online but didn't come across a definitive answer...

If my character is a multiclassed spellcaster, can he learn the same spell from two different classes?

For example, he is a level 3 Bard and a level 1 Wizard. One of his first Bard spell choices was Sleep. When he multiclasses into Wizard, he decides he eventually wants to replace Sleep with another Bard spell, but still wants to have Sleep be available via his small list of Wizard spells (as he only plans to take one level of the class.) Can he learn Sleep as one of the six starting Wizard spells in his spellbook, while it's still available to him as a Bard spell as well?

I think so.

The known spells when multiclassing follow the same rules as for the single classes singularly. Each spell you know and prepare is associated with one of your classes, and you use the spellcasting ability of that class when you cast the spell.

There is no reason why you couldn't. Also, bard and wizard spells are learned differently. Wizard spells are written down while bard spells are memorized. A wizard can change their prepared spells based on the contents of their spell book. Also, keep in mind that even if you don't take sleep as one of your initial  wizard spells that if you come across a scroll of sleep later in your travels you can always transcribe it to your spell book.

Everything seems to rule in favor of this possibility;

From the multiclassing rules:

Spells Known and Prepared. You determine what spells you know and can prepare for each class individually, as if you were a single-classed member of that class.

and

Each spell you know and prepare is associated with one of your classes, and you use the spellcasting ability of that class when you cast the spell.

So yeah, this would totally work. You might even throw in some fluff about how the magic works differently and how your character experiences that.

Thanks. I suspected it should be OK, but wasn't sure.