Can you pay additional costs like kicker after a spell has been put on the stack?

No. When you cast a spell, the entire casting process happens in a defined sequence under CR 601.2. During this process, you announce the spell, make all choices (including whether to pay optional additional costs like kicker), and then pay all costs. Only after all of this is complete does the spell actually become 'on the stack' in the sense that players can respond to it.

Specifically, CR 601.2b requires that you choose whether to pay any optional additional costs at the time of announcement. CR 601.2f then requires that all costs are paid simultaneously. Once that payment step is complete and the spell is fully on the stack, you cannot go back and add or change additional costs — that window has closed.

This means if you forgot to declare kicker while casting your spell, you cannot retroactively pay for it after the fact. The decision is locked in during the casting process, not after. This applies to all additional costs: kicker (CR 702.33), multikicker, entwine, buyback, and similar mechanics.

Example: You cast Goblin Bushwhacker and complete the casting process without paying the kicker cost. Your opponent says 'OK, it resolves.' You cannot then say 'Wait, I want to pay the kicker now.' The spell is already on the stack and that moment has passed.

If you genuinely forgot and both players agree the game is still in a state where it can be backed up (e.g., in a casual game), that's a social decision — but under the rules, the kicker choice is irrevocably made during casting.