A counterbalance loom is limited to tieups that pull at least some of the shafts downward when raising others. I have only used "balanced" tieups that lower and raise pairs of shafts together, though I have read that unbalanced tieups can be used with counterbalance looms.
In order to use arbitrary tieups and maybe add a few shafts, I have been converting my loom to countermarche. The mechanism is kind of a neat thing to build, with pulleys and levers and a lot of control cords. I would like to try shaft-switching at some point, so I went with vertical jacks so that there is no lamm cord through the center of the shafts. Now that I have a lathe, this pulley method is a good way to make them. Here they are still spinning:
then with some danish oil...
I think my old Swedish Gesta Snikerifabrik is a very common floor loom design. Here are a few measurements I took to build additional lamms, jacks and shafts:
Lamm: 5/8" x 1-5/8" x 57" Between left & right uprights (inside dimension): 1-1/2" Left/Right Upright Thickness: 1-1/2" Shaft rod: 7/16" x 1-1/4" x 55" Pulley: 1/2" x 1-1/2"
Here is the new pulley holder with the first jack tied only to the first "long lamm". I made the jack the same dimensions as the lamms with 12" between the axel and the shaft coords and another 12" up to the lamm cord. This is a lot bigger than it needs to be.
Here are the first two jacks in place, showing the pulleys from the lamm side.
I used 11" instead of 12" for the third jack, but it can probably be a lot smaller.