This only works for three inputs, but love the Raven Labs MDB-1 for this purpose.
Practically speaking, three is normally the maximum I've contemplated using on one gig anyway, although "which three particular basses" can and does change.
Eg for the Steely Dan project I lead it's mostly my '74 PBass with one or two tunes done on either my Reimer or my FBass (damn you Donald Fagen and your vocal-range-driven key change on Josie!); for something like Gabriel Palatchi or for my jazz quartet it might be my Reimer and my UBass with one or two tunes on the FBass. Soon it'll be "any two of these plus a fretless". Realistically I'd prefer 6 presets so I can have a named preset stored for each one, but I'll start by attacking the "show must go on" needs first and worry about luxuries next.