Well, where does the other PC wizard's spells come from? Presumably not mailed to them from their Master.
In the AD&D Dungeon Master's guide, DMs are advised that Magic-Users (now called Wizards) will need to do one of three things to gain more than the one spell per level they received in that edition: independent research, trade spells with other [wizards], or find them in treasure hordes. The older edition also had a training requirement between levels, so I always assumed (in re-reading now I see no supporting evidence for this) that during level training the [wizard] was researching new spells, which would ultimately become the ones they learned when they achieved a new level.
The original DMG (OG DMG?;)) also points out that PC [wizards] will naturally trade spells, but that NPC wizards will jealously guard their spells from PC wizards. Perhaps your wizard then traded a spell with another wizard they met at a bar or library? As an aside, this is actually the second advantage of multiple PC wizards (beyond the obvious extra spells slots per day for the party) is that each wizard brings a more diverse spell pool to the group. Where before you were limited to two spells per level, now you get to choose four, which brings more options to the group.
If your DM levels you up around the time you find a big treasure horde (at the end of an adventure) maybe they can work in that you find a spellbook and copy the spells from there. As a DM I often use spellbooks as treasure.
In the 3rd Edition Forgotten Realms supplement "Magic of Faerun" presented the mage guild as a source of new spells, adding extra spells per level at the cost of membership dues (role-played and mechanical). City of Splendours (also a Forgotten Realms supplement) presents some other "Mage Guilds" which provide extra spells known per level. These are presumably the result of access to Guild owned spellbooks and the Guild's well stocked research library. In my own games, I push the Guild membership on my PCs to justify how they learn new spells if they don't come up with something better.
TL;DR wizards can explain learning nEw spells each level by a variety of means, including but. It limited to independent research, finding them in old tomes, copying them from the Wizard's Union local library, or swapping them with other spellcasters they meet in their travels.