Can you pay an alternative cost and additional costs at the same time?

When you cast a spell, you determine its total cost before paying (CR 601.2f). The total cost can include an alternative cost plus any number of additional costs. An alternative cost replaces the spell's normal mana cost, but it does not interact with or prevent additional costs from being applied (CR 601.2b, 601.2f).

Additional costs are costs declared separately from the mana cost — things like kicker, buyback, or a cost imposed by another card (e.g., "as an additional cost to cast this spell, sacrifice a creature"). These stack on top of whatever cost you are paying (mana cost or an alternative cost) to cast the spell (CR 601.2d, 701.33).

One important restriction: you may only apply one alternative cost to a spell at a time (CR 601.2b). You cannot layer multiple alternative costs together. But pairing a single alternative cost with one or more additional costs is perfectly legal.

Example: You control a card that lets you cast your next instant or sorcery for free (an alternative cost of paying 0). You cast Momentary Blink using that free alternative cost, and you also pay its flashback cost — wait, those are both alternative costs, so that wouldn't work. Instead, picture casting Root-Kin Ally (which has a convoke mechanic acting as a cost reducer) alongside an additional cost imposed by a card like Thalia, Guardian of Thraben. More cleanly: cast Force of Will using its alternative cost (exile a blue card + pay 1 life) while also paying an additional {1} tax imposed by Thalia. Both are paid simultaneously when you announce the spell.

In summary, alternative cost + additional costs = allowed. Multiple alternative costs on the same spell = not allowed (CR 601.2b).