Technically? A marine can take as much as they want in the form of additional ammo clips.
Take a look at the MK6 schematic:
The ammo clip is a small little package in the bottom right that's affixed to the marine's utility belt. There's no space in the backpack as that's a power supply, nor is there space in the rest of the armour.
In the old Rogue Trader days, 40k players would get plastic marine sets that allowed you to make some ridiculously ammo-laden marines:
You could put as many ammo packs on the marine as you liked (or as you were able to get to stick via contact cement!).
Contemporary marine models generally are depicted as carrying one or two ammo packs at most. There does not seem to be much clarity to their ammo loadout in either models or fiction beyond the fact that most marines are well-equipped for whatever the expected length of the engagement is. Going to secure a dropzone? Carry a loaded bolter. Going in for a long-term Hive purge? Hitch as many clips to your belt as you can carry.
BTW, also keep in mind that Marines generally have the best logistical support of any troop in 40k. Rhinos, Land Raiders and Drop pods all provide forward supply depots of additional ammunition for long-term field deployment.
- Marine's can carry as much ammo as needed for the mission plan on
- In cases where more ammo is required, Marines can carry more
on their suit's belt or rely on the Imperial war machine to provide
long-term mission support.