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For maximum possible cantrips, you take Mage Initiate and Spell Sniper, 4 levels in warlock, 1 level sorcerer, 1 cleric (Arcana), 2 druid (circle of the land), 1 wizard, 1 bard, 4 levels in eldritch knight fighter and 4 levels in arcane trickster rogue. Also, you can get one extra cantrip from racial bonuses form genasi, high elves and tieflings. It's horribly sub-optimal, but it gives you 29 cantrips in total. Also, you can get one extra cantrip from racial bonuses form genasi, high elves and tieflings.

For maximum possible cantrips, you take 1 level sorcerer, Mage Initiate and Spell Sniper, 4 levels in warlock, 1 cleric (Arcana), 2 druid (circle of the land), 1 wizard, 1 bard, 4 levels in eldritch knight fighter and 4 levels in arcane trickster rogue. Also, you can get one extra cantrip from racial bonuses from genasi, high elves and tieflings. 

It's horribly sub-optimal, but it gives you 29 cantrips in total.

For maximum possible cantrips, you take Mage Initiate and Spell Sniper, 4 levels in warlock, 1 level sorcerer, 1 cleric (Arcana), 2 druid (circle of the land), 1 wizard, 1 bard, 4 levels in eldritch knight fighter and 4 levels in arcane trickster rogue. It's horribly sub-optimal, but it gives you 28 cantrips in total.

For maximum possible cantrips, you take Mage Initiate and Spell Sniper, 4 levels in warlock, 1 level sorcerer, 1 cleric (Arcana), 2 druid (circle of the land), 1 wizard, 1 bard, 4 levels in eldritch knight fighter and 4 levels in arcane trickster rogue. Also, you can get one extra cantrip from racial bonuses form genasi, high elves and tieflings. It's horribly sub-optimal, but it gives you 29 cantrips in total. Also, you can get one extra cantrip from racial bonuses form genasi, high elves and tieflings.

For maximum possible cantrips, you take Mage Initiate and Spell Sniper, 4 levels in warlock, 1 level sorcerer, 1 cleric (Arcana), 2 druid (circle of the land), 1 wizard, 1 bard, 4 levels in eldritch knight fighter and 4 levels in arcane trickster rogue. It's horribly sub-optimal, but it gives you 28 cantrips in total.

Edit: @Neil Slater pointed out Arcana Domain gets more cantrips. Changed to show for it.

For maximum possible cantrips, you take Mage Initiate and Spell Sniper, 4 levels in warlock, 1 level sorcerer, 1 cleric (Arcana), 2 druid (circle of the land), 1 wizard, 1 bard, 4 levels in eldritch knight fighter and 4 levels in arcane trickster rogue. It's horribly sub-optimal, but it gives you 28 cantrips in total.