Question

If I have a Pokemon holding the item Metronome and I have the Pokemon use a Multi-hit move (EG. Bullet-seed) would the metronome power each hit up? Or would it be every time I use the move?

Answer 1

No, it's every time you use the move.

http://pokemondb.net/pokebase/39919/double-hit-with-metronome
http://pokemondb.net/pokebase/40528/metronome-item-and-multiple-hit-moves

Answer 2

The boost is only applied on multiple selections of a move, not multiple executions. This means that moves that lock the user into the move for multiple turns will not boost for each time the user attacks, only when they select the move again.

When you use the move.

Source

Answer 3

Multi-strike moves are counted by the number of turns on which they are used, not the number of hits made.

Source: Bulbapedia/ Metronome

So it counts everytime you command your Pokemon to use the move, not how many times it hits in one turn. That would be OP.