Mauxir can be used as a generic support for all operatives, allowing them to deal damage to Kebachet from Mauxir's Support Skill to deal extra damage to an enemy.
Note that Mauxir's Support Skill deals continuous Chaos-damage, so if you're using both Mauxir and Vidya - Celestial Swan, you will want the main dps to also deal Chaos damage.
Mauxir works best as a ballistic damage support, buffing ballistic operatives via her M1, weapon effect, and logistics set.
As such, Mauxir works best with ballistic operatives, ideally ones with a high damage-per-shot and low-RoF to gain the most benefit from her Deiwos passive.
Ideally operatives that use a shotgun or sniper, to maximize her M1, but pistols gain a lot of benefit too:
Yao - Winter Solstice
Bubu - The Geomancer (Note that Bubu has 100% crit chance for her ult anyway, so she gains less benefit from the added crit rate from Mauxir's M1.)
Mia - Starchaser (Note that Mia has 100% crit chance anyway, so she only benefits from the Crit Dmg Amplifier and damage transfer, not the extra crit rate)
Fenny - Coronet (Note that Fenny has a naturally very high crit chance anyway, so she doesn't gain much from the extra crit rate from Mauxir's M1)
Basically any operative that deals a lot of damage with slow-firing shots.
Mauxir does also work with ballistic operatives with higher fire rates, but the effect of her Deiwos passive will be reduced.
If you don't much care about her Deiwos, then you'll want to use Mauxir with operatives that deal ballistic damage, ideally from a sniper or shotgun, or maybe pistol, to maximize the effect from Mauxir's M1 buff, however Mauxir still works well for all ballistic-damage operatives.
Mauxir can also be used to provide a stationary target, which is useful for operatives that have trouble hitting highly-mobile enemies:
Fenny - Coronet
Coronet has a short range, so highly mobile enemies can be a problem for her - A problem that Mauxir can solve.
Haru - Raikou
Raikou is a skill-dmg operative, but the stationary target can be really useful to her.
Raikou also deals Chaos-damage herself, allowing Raikou+Mauxir to be used with Vidya - Celestial Swan.
Cherno - Enigma
Enigma is a skill-dmg operative, but the stationary target can be really useful to her to allow her voids to consistently stay on top of an enemy.
Enigma also deals Chaos-damage herself, allowing Enigma+Mauxir to be used with Vidya - Celestial Swan.
Nita - Pulse
Enigma is a skill-dmg operative, but the stationary target can be really useful to her.
Haru - Absconditus
Absconditus is a skill-dmg operative, but the stationary target can be really useful to her.
Skill-damage operatives won't benefit from Mauxir's Amarna logistics squad, or her crit buffs, but the stationary target can allow them to deal much higher damage by virtue of just being able to more consistently deal damage themselves by just hitting the stationary target from Mauxir's support skill.
Mauxir can still use the Twilight logistics squad to debuff enemies Chaos Resistance, which is useful for dps operatives that deal chaos damage themselves.
If they don't deal Chaos-Damage, then Mauxir won't be able to use a logistics set to provide skill-damage operatives much benefit at all, meaning Mauxir provides a stationary target that increase their damage a bit, some ATK buffs from Mauxir's weapon, and not much else.