MOTs in series

["Tesla list" <tesla@xxxxxxxxxx>]

Hello,

This is probably a stupid question, but I was wondering what exactly the
problem with having several MOTs in series is.  The web sites that I
have found that discuss this topic all say that the problem is that the
insulation on the secondary isn't sufficient to prevent arcing to the
core, but what if the core is at high voltage as well?  Like, if the
secondaries were strung together, with the hv output of one secondary
attached to the core of the next MOT?  I think that each MOT would
not have a potential difference from the secondary to the core of more
than the original rating for a single MOT, and since the primaries are
electrically isolated from the high voltage across the secondaries,
arcing to them shouldn't be a problem, unless maybe something on the
secondary was grounded.  Is this correct?
Also, I was wondering if you could parallel the primaries instead of
connecting them in series, so that different MOTs could be connected to
different outlets/circuits/breakers (assuming they were all
in-phase).

Thanks a lot,
Chris