I've become somewhat of a botanical bulb fanatic (if you haven't figured that out yet), with lilies and other genera. I have much to say, whether you're interested or not.
Too much for a single post, so I'll sprinkle it around.
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Definitely, do not try to manually break a multiple nosed bulb apart if it doesn't have a naturally weak breaking point.
Some lilies have tall and wide (read: massive) basal plates that simply will not break by hand. Attempting to do so results in a naked basal plate and a multitude of broken, individual scales. The remedy, sometimes, is to let the mother bulb grow a few more years when it will naturally produce a weak, breaking point for bulb separation. Other times, this just never happens, and the only option is to knife cut the basal plate from the bottom and perhaps half way up (or more), to produce the weak breaking fissure that one can then finish manually breaking by hand.
In most cases, try
not to completely cut the division with the knife. Where ever the bulbs break naturally will be the best separation point, because of both strength and natural pathogen resistance. In other words, if there is a naturally weak point in the basal plate, that is the healthiest place to separate. Cutting with a knife, even a millimeter off of the natural break point can make a difference. Although it is almost never critical, the best practice is to let mother nature guide you.
This, of course, is assuming the mother bulb is healthy. A weak point cause by mechanical damage or disease would not be a
natural weak point.