The best example I know of is Freebass, a short-lived collaboration between Mani, Peter Hook and, erm, the bassist from the Smiths.
The band in the OP seems very jumbled to me (and the clank/fretnoise does my head in) but here some thought has gone into keeping the roles separate, it's not three basses in the same register, all playing at the same time, all of the time, like three stoned bass players at a rehearsal studio.
Here's a dubby track with the other players noodling a bit over the top:
http://youtu.be/jhRv2xrlCPU
Saying that, most of the album is just mediocre indie rock
My conclusion? Multiple bass player bands tend to be an idea that they try to make work, rather than being a format which is naturally conducive to creating great music. All good fun though