Is there any way of increasing deck space without ranking up? I keep getting disabled by people who seem to have way more stuff than they should. I must be missing something.

From arti drops you get rescued prisoners and ship-bots. Those both help to increase decks.

You can get Ship-bots (add +2 decks to your ship) from your artifact planets via Trade tab or get the Lazuli Parts Vault as a drop from Lazuli Titan, a boss npc.

Please remember this: More decks, more damage you receive from a larger enemy ship!

No, it's more decks, more damage you recieve from ANY enemy ship. assuming your deck is more than rank+19, otherwise the dmg cap stay the same XD

but yeah, you can get rank points and decks from a few other sources, including GP, mission, NPC and artifact pulls.

The Sillix race also gives 50% more decks, so that could be why you're seeing so many extra modules on their ships.

Chloror, better check your facts and figures before posteing. SILLIX is only TEN(10%) extra decks.. if you got 50% youd be able to have EVERYTHING researchable, by the time your ~rank 250-300

and that's a bad race....
you can get more stat boost out of one of the other races w/o raising ur dmg cap...

for example, run a aerlon and run 2 fewer def module, or konquel with 2 fewer weapon module etc...