Can you redirect the target of a spell to a different legal target after it's been cast?

When a spell or ability is cast and its targets are chosen, those targets are locked in at that moment (CR 601.2c). Players cannot simply decide to change targets after the spell has been placed on the stack — the game does not allow free retargeting.

However, certain spells and abilities explicitly grant the power to change a target. Cards like Redirect or Fork (and similar effects) let a player choose a new legal target for a spell or ability on the stack. When such an effect resolves, it changes the target to the newly chosen one, as long as that new choice is a legal target at that time (CR 114.6).

Additionally, the controller of a spell or ability may change its targets when that spell or ability is 'retargeted' by effects that say 'change the target.' The new target must be a legal target — it must satisfy all targeting restrictions the spell originally imposed (CR 114.6b).

Concrete example: Your opponent casts Lightning Bolt targeting your creature. You cast Redirect targeting that Lightning Bolt. When Redirect resolves, you choose a new legal target for Lightning Bolt — say, your opponent's own creature. Lightning Bolt now targets that creature instead and will deal 3 damage to it when it resolves.

Outside of explicit effects like this, targets cannot be changed after they are chosen. If all targets of a spell become illegal before it resolves, the spell is countered by game rules (CR 608.2b).