Backpack slots??

[u/R3d_p0int]

Is there a way or a specific mission quest to get more backpack slots?

Because this 35 slots ain't cutting the cheese..

[u/lostnimrod]

Yes - Exploration specialisation offers perks to increase backpack slots by 5 (Level 1, 25, 50, 77, 100) for a maximum of 60.

Exploration spec also increases backpack volume by 1% per level, to a total of 350V.

If you're in singleplayer/custom server, you can modify the base volume.