Does each hit of a multi-hit attack increase the power of the move Rage Fist?
Rage Fist inflicts damage. Its power increases by 50 each time the user was hit during a battle (including times the user hit itself in confusion), up to a maximum of 350 (after 6 hits), with each strike from a multi-strike move counting as one hit.
Yes, Rage Fist's power does increase for each multisrike move that hits.
Source: https://m.bulbapedia.bulbagarden.net/wiki/Rage_Fist_(move)