A Staff of the Magi has the Spell Absorption trait (emphasis mine):
While holding the staff, you have advantage on saving throws against spells. In addition, you can use your reaction when another creature casts a spell that targets only you. If you do, the staff absorbs the magic of the spell, canceling its effect and gaining a number of charges equal to the absorbed spell's level. However, if doing so brings the staff's total number of charges above 50, the staff explodes as if you activated its retributive strike (see below).
The staff also allows you to cast several spells at-will (emphasis mine):
You can also use an action to cast one of the following spells from the staff without using any charges: arcane lock, detect magic, enlarge/reduce, light, mage hand, or protection from evil and good.
Can two creatures – each with a Staff of the Magi – take turns casting enlarge/reduce on each other, regaining two charges per round? Is there some reason why this wouldn't work?
A reasonable response to this would be "how did two characters get the same legendary magic item?"
Unfortunately, Season 8 of Adventurers League allowed any Tier 3 or higher character to purchase one. Barring edge cases, any character that played three 4-hour sessions at Tier 3 or 4 (enough to level up one-and-a-half times) could grab a shiny new Staff of the Magi off the shelf.
Season 9 removed the ability to get them (without encountering one in an adventure) and made legendary items Tier 4-only, but there are still a lot floating around.
This question is related to "Can an ally charge your Staff of the Magi before a long rest by casting a bunch of spells at you?" The difference is the source of spells. Some magic items, like a Ring of Spell Storing, interact differently with spells cast from spell slots vs magic items. I want to make sure I'm not missing any pertinent details.