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

When you cast a spell, you may pay an alternative cost (such as Flashback, Overload, or an opponent's offering effect) instead of the spell's mana cost. Crucially, paying an alternative cost does not lock out additional costs — you can still pay those on top of the alternative cost. This is explicitly supported by CR 601.2b, which states you choose one alternative cost if any, and then any number of additional costs.

Additional costs are things like Kicker, Buyback, Entwine, or costs imposed by other cards (e.g., "as an additional cost to cast spells, sacrifice a permanent"). These stack on top of whatever base or alternative cost you are paying. CR 118.9 confirms that additional costs are paid alongside, not instead of, the chosen cost.

One important restriction: you may only choose one alternative cost per spell (CR 601.2b). You cannot, for example, pay both Flashback and Overload on the same spell. But pairing a single alternative cost with one or more additional costs is perfectly legal.

Concrete example: You cast Snapcaster Mage and give a Lightning Bolt in your graveyard Flashback. If a Thalia, Guardian of Thraben is on the battlefield, she imposes an additional cost of 1. You pay the Flashback cost (R) as your alternative cost, and also pay Thalia's additional 1 — both costs are paid simultaneously when you cast Lightning Bolt via Flashback.

So in summary: one alternative cost + any applicable additional costs is always legal. The rule that forbids stacking is only about choosing multiple alternative costs at once (CR 601.2b).