FG the way I look at it there is more than three families, so if you have 3 beds but want to grow 2 crops per year, why not look at a 6-crop cycle or something like that i.e. separate out potatoes from carrots and other roots, make alliums into a new family group by themselves, introduce cucurbits and/or sweetcorn and/or catch crops into the plan - that way you can be sowing and planting all year round, two or more crops a year from the bed, each crop from a different family, for 3 whole years. And if you get stuck for overwintering crops, stick on a green manure to keep it going.
I'm trying to work out a plan for the next year or so based on the above, with the added advantage that I haven't yet decided how many beds I will have. The current idea is 6 rotation beds plus another area for permanent and mixed planting, but if I can't come up with a rotation plan that allows me, at least in theory, to keep all areas in use at all times then I might rethink. (I'm not expecting to get everything in use all year round just yet, I just want to have a Vision For The Future...)
It's all frying my brain a bit - and on the whole I'm quite attracted by the Snadger approach to rotation (i.e. don't follow like with like, otherwise don't worry too much about it). I just want to make sure I have things growing as much of the year as I reasonably can.