I haven't seen many of the big sleeper rigs except on bed buggers and maybe a couple o/o independants who just select light loads.
"It is not the critic who counts,
not the man who points out how the strong man stumbled,
or where the doer of deeds could have done better.
The credit belongs to the man who is actually in the arena;
whose face is marred by the dust and sweat and blood;
who strives valiantly; who errs and comes short again and again;
who knows the great enthusiasms,
the great devotions and spends himself in a worthy course;
who at the best, knows in the end the triumph of high achievement,
and who, at worst, if he fails, at least fails while daring greatly;
so that his place shall never be with those cold and timid souls
who know neither victory or defeat."
car haulers, moving vans, flat beds, dry vans, refers... there are big bunks pulling all kinds of freight.
You won't likely see big bunks pulling tankers- bulk or otherwise.
A big bunk- depending on the setup- can weigh anywhere from 24,000 on the low end to upwards of 30,000. That's leaving out 90 inch sleepers which are just a step up from a regular bunk. I don't call it a big bunk unless it has at least 120 inches of sleeper. 30,000 lbs is a massively heavy big bunk- you're most likely to find them weighing 26,000-28,000. That's been my experience from talking to other big bunk owners.
I've recently seen big bunks with Fedex (non-carhaul and carhaul), Landstar, Air Ride and many other traditionally non-big bunk companies.
Most of the large sleepers I have seen are usually pulling a flatbed.
Either Landstar or Mercer. You might want to start making some calls to different companies and get your info straight from the horses mouth though. That's the best way to find out for sure if they will accept one.
I would say that, weight aside, the limiting factor for most o/o when it comes to big bunks is the price. Many companies don't pay their o/o well- FAF is one that has been mentioned in this thread. Their rates are very low for o/o. And to support a truck payment is hard enough- add the price of a custom sleeper and you might just be asking for problems.
Even used big bunks (if you can find one that's not already off the market) are pretty pricey.
ARI, ICT and Double Eagle are very, very proud of their products. The average ARI sleeper costs more than my house did. Granted, it's a small house in the middle of nowhere...