An army like this is definitely possible, and even flavorful! Space Marine chapters definitely move and fight separately most of the time. However, during crusades, the forces of the Imperium band together in great armies and mix it up. Thus, an army composed of many different Chapters is most likely a Crusading army. Such an army would be pretty cool, and you could go to town with different chapters joining in on the fun. Of course, some chapters have big grudges against other chapters (Space Wolves vs. Dark Angels come to mind), but most of these chapters have their own Codex anyways, so you wouldn't be able to field them with normal Marines.
Crusading units could come from any chapter, but here are some suggestions:
- Imperial Fists
- Raven Guard
- Black Templars (they're the quintessential crusading chapter, and they have their own codex, but you could use Sword Brethren as Vanguard Veterans and stick 'em in a Land Raider Crusader and call it a day).
- Any other frickin' chapter you can find or dream up! An army like this is a great excuse to come up with sweet backgrounds and color schemes!
On the other hand, if you're looking for a "lost in the warp" kind of feel, none of the well known chapters would really give you the image you're looking for. There was a Chapter Approved article in White Dwarf some years ago that talked about "cursed Chapters," or Chapters that for some reason or another got unlucky or fell from grace. Most of these chapters have disappeared into the Warp or have otherwise fallen off the grid, so these cursed chapters might be just what you're looking for. If you made a force of these Marines your army would truly be unique!
I can't remember all of the Chapters involved, but here are a few:
- The Lamenters
- The Fire Hawks
- The Legion of the Damned (this Chapter is especially appropriate, because they have their own army list entry now, and they're hard as nails!)
If the "cursed Chapter" thing is more of what you're going for, I could dig through my stacks of WD's and see if I could find that issue for you.
Hope my advice has given you some ideas!