  Moyal-deformed hierarchies of soliton equations can be extended to larger
hierarchies by including additional evolution equations with respect to the
deformation parameters. A general framework is presented in which the extension
is universally determined and which applies to several deformed hierarchies,
including the noncommutative KP, modified KP, and Toda lattice hierarchy. We
prove a Birkhoff factorization relation for the extended ncKP and ncmKP
hierarchies. Also reductions of the latter hierarchies are briefly discussed.
Furthermore, some results concerning the extended ncKP hierarchy are recalled
from previous work.
