You can upgrade your SL (shot level) 4 times, up to level 5 here they are:

SL 1

SL 2

SL 3

SL 4

SL 5

SLevel restrictions

You cannot fully upgrade it even if you know where the power up spawns, because the game "locks" your lvl in certain stage intervals.

If you reach the interval limit, upgrade spawns become golden orb spawns, and these are the intervals and their respective limits

Solaria ~ Ash - lvl 2 max

Hexol ~ Virion- lvl 3 max

Ferrinar~ Iris- lvl 4 max

The Lair is the only stage you can get up to lvl 5.