Can you cast spells between the first strike and regular combat damage steps?

When one or more attacking or blocking creatures have first strike or double strike, the combat phase includes two separate combat damage steps (CR 310.1, 509.1). After the first combat damage step resolves, the game moves to a new phase of priority passing before the second (regular) combat damage step begins.

According to CR 509.4, after combat damage is put on the stack and resolves, players receive priority again in turn order before moving to the next step. This means that after first strike damage is dealt and state-based actions are checked (potentially killing creatures), each player gets the opportunity to cast instants, activate abilities, or take other actions before regular combat damage is dealt.

This priority window is significant because creatures that die from first strike damage will not deal regular combat damage. Players can also cast pump spells, removal, or other instants during this window to affect which creatures survive into the regular damage step.

Concrete example: Your 2/2 first striker is blocked by your opponent's 3/3. In the first strike damage step, your 2/2 deals 2 damage to the 3/3. Before the regular damage step, you cast Giant Growth (+3/+3) on your 2/2. Now in the regular damage step, your 5/5 deals 5 damage to the 3/3, which already had 2 on it, destroying it — and your creature survives because the 3/3 never got to deal its 3 damage back.

Note that if no creatures have first or double strike, there is only one combat damage step and no such intermediate priority window exists (CR 310.1).