Your faction is plenty. As far as Comps go, your done with that. You should be talking to either Scuti/Telum/Vegato (No name shown), for any further missions in Stage II.
Questions.
Did you do all of Stage I in its entirety for I'm assuming a PP (Shields/Reactors/Weapons)? Way to quickly know is you received a Expert Builder card for each discipline and a symbol of loyalty, plus there are several prints that would be under the PPs belt as well majority of all this stuff is at the very bottom of build list (so makes it easy to find.
STAGE I - PP
Comps - L1 Collegia Research Authorization MXXIC, L3 Hull Mesh Laminate III
Shields - L3 Skirmish Shield I, L2 Amplector Omega, L5 Seco Secare Secui Sectum Quinque, Stage II Invite - Shields
Reactors - L5 Auctoritas Remoror Quinque, Stage II Invite - Reactor
Weapons - L2 Calthius Omega Beam, L5 Multiforus Multiplico Effervo Quinque (MMEQ) PL, Stage II Invite - Weapons
Ammo - L2 Blowgun Toxicum Dart, L5 Effervo Flechette
Kicking off some of the missions requires you to have specific items that are detailed from a prior missions ending talk tree. The NPC giving the mission isn't gonna tell you what you need to get him to talk as you were suppose to catch that info from the last NPC. Just remember ALL this stuff connects, missions, all progens, all items etc. Its a giant spiderweb of interwoven pain lol. My advice is always have double-triple of each thing requested/doing at every step o the way cuz you will most likely need it again.
Find myself or several other folks in game who can provide guidance/assistance with the missions as we've all gone thru the pain chamber and completed these from Stage I,II and III.