Like a bunch of the others, I'd say the Scrapivore to pair with the B6 LE. At their low price point, you could get a Scrapivore then either put a handle on yourself or have someone do it for you and still be on the cheap side of frugal.
When I think of pairing knives, especially in a piggyback config, I anticipate a significant size/function step between the pair. IMHO the step between a B6 LE and a 311 isn't very large. They're a small-size-medium and a size-small knife pair. Hence my recommend for a 'vore to establish a significant step between the two knives you're carrying. JMHO and YMMV.
That said, since it sounds like you already have a 311 in hand, I hope you enjoy the heck out of using it. Let us know how it works for your purposes.