What you're talking about is not
bi-amping, splitting a single source signal (PA, bass guitar, etc.) at a certain crossover frequency into dedicated amps and speakers for lows and highs. This was done in bass guitars in the 70's and 80's, and for most, its time has come and gone with the advent of current technology. Modern amps and cabinets have made it unnecessary these days. I did it back in the day, but would not now.
There are lots of cabinets with several different size speakers in them (PA bins, home hi-fi, lots of bass guitar cabinets) driven off single amps, but these used
passive crossovers inside the cabinet (an electronic circuit) that divides and sends the right frequencies to the right speaker inside the cabinet.
Now, some guys may still bi-amp for effects following the technique that you leave your big fundamentals, the low end of the split, unaffected and clean, then use the upper part of the signal for the applied effects (chorus, distortion, etc.). We see this practice followed electronically in some bass pedals, and you can still use your regular amp and cabinets with those.
You're talking more about a split signal (which can be done with any bass, not just Rickenbackers, with a 'Y' cable) where you're split-sending signal to a bass amp for your bass tone, and generally a smaller guitar amp for distortion, from the bass guitar. This would be easier than trying to do this with splitting cabinets off one head, by far, which most likely wouldn't work, two amps work best for this. Sending big bass through guitar cabinets is generally a recipe for disaster at any kind of loud levels: They're generally not built for that.
Now you could do this with a Rickenbacker with the separate outs, but don't get confused by those: Those outputs aren't 'stereo', nor are they after a crossover inside the bass. It's actually an output for each pickup. So you could use the neck pickup to drive a bass amp (the deeper sounding of the two) and the bridge pickup for the guitar amp and effects (the thinner sounding of the two). One bass, two cables, two amps, but you'd have to match the amps so one would not drown out the other.
I'd also advise steering clear of old Sunns or any of the other ancient sleds: Unless they're VERY properly maintained, they were built for a different time . . . . . a long time ago. What slightly different preferred tone you might think you hear would be far outweighed by maintenance headaches for those of us that aren't touring with guitar roadies and electronic techs. I'm old enough to have used a lot of the ancient 'lead sleds' back in my time, and would NOT trade them for modern gear.
Here's one of the 'Rig Rundown' vids from
PREMIER GUITAR about Stanley Clarke's touring rig from 2011. SC was running a small Fender guitar amp for a distortion edge on some tunes, and here his tech explains how they did it, right around the 3:00 mark:
Rig Rundown - Stanley Clarke
The two Alembics run off 18v phantom power (those big plug-in cables on the face of the two Alembics just below the knobs), and the 'preamps' his tech is talking about are actually Alembic DS5R power supplies for each bass in the top rack. These have HIGH, LOW, and FULL RANGE outputs, and for one of the amps, they tapped the HIGH output (while still feeding the Ampeg heads simultaneously from the FULL RANGE output) to go to that Fender amp for one of the Alembics. Mic'd up thru the house and monitors, it's 'big enough'. It's similar to the Rickenbacker setup, the HIGH is the bridge pickup, the LOW is the neck pickup, and FULL RANGE is both pickups.
Now most of us don't have the advantage of touring with a trunk full of Alembic gear, but this illustration of the idea is what you want to take away for the best way to do this: Ideally, to feed a signal short of the deep end of the signal to a suitable guitar amp.
There's several ways to do it, and you'll have to decide what's best for you.
AND . . . . . however you do this, MAKE SURE you've got it squared away and it WORKS, every time. The surest way to lose gigs is to show up with some half-ass, only-works-if-I-hold-my-mouth-just-right rig that you're fighting all night long to keep it running. Mess up like that on a regular basis, and you'll be back gigging in the bedroom so fast you won't believe it. Being a pro and green are NOT mutually exclusive, and very few will give you time to grow up on the bandstand. With the real musicians, being prepared is an expected given.