ok, xs1100's , ive a bit of experience as my mate has one and has had the same problems at various times in the past. firstly, the xs100 ignition system was designed by the universal guild of points ignition manufacturers as a sick joke to prevent people from fitting cdi units to bikes!! i kid, but only a bit. the ignition system is unique in having 2 seperate mechanical ignition advance/retard units on it. one is mechanically operated by bobweights on the ignition pickups, the other is vacuum operated from a pipe connected to the carb inlets. quite why yamaha decided to simplify the ignition by fitting a cdi, and then complicate it by fitting such a dogs dinner of adv ret units is beyond me. anyhow, i digress. the pots fire in pairs, however, they fire in 1+4 and 2+3 together, not 1+3 and 2+4. the carbs can be a pain as they have 2 seperate fuel taps, one feeds 1+2 the other 3+4, and both are vaucuum operated, so if the vac pipe for cylinders 1+2 is off, then those 2 pots will fail, ditto the other tap. if the ignition coils went tits up, then you would lose either the two outer post or the centre 2, so that may help narrow things down. the ignition system is further complicated by the coils not actually being 12volt, but actually 9 volt, these are boosted on startup to 12volt, but ballast resisters then make them run on 9volts i told you it was a dogs dinner didnt i. chuck in the fact that when the ballast resistors go tits up, you wont know , but the coils will slowly overheat and cut out eventually! this can in time cook your cdi unit, which, living under the seat at the back, can also cop a soaking from the back wheel! xs11 cdi's are like hens teeth.
remember also that XS1100's have an anti fall engine cut out on them. this is a tilt switch that is designed to kill the engine if the bike falls over. this is fine on a solo, but on an outfit, the bike actually experiences sideways forces that can cause the ignition to cut out mid corner(from experience this!!) so disconnect the cutout if you havent already.
finally, check the drain hole in the recess for the petrol filler cap. this can easily clog up, allowing water to collect in there, then when you open the petrol cap, the water spills over into the tank, contaminating your fuel. rusting the tank and then clogging carbs with rusty dust.
xs1100 carbs are also a bit cack, we fitted fj1200 carbs to daves, which had the twin benefits of making it both faster and also improving the fuel consumption!!
id clean and gap the plugs, and check all the connections first, then check the adv ret are working. next, id check the carbs on the left side, drain them and see if they have any water in them. if so, id check the filler cap, and then drain the tank and clean it out, perhaps even seal it too.
good luck!!