  The treatment of time-dependent dynamics of quantum systems involving
multiple states poses considerable technical challenges. One of the most
efficient approaches in treating such systems is the Morris-Shore (MS)
transformation which decomposes the multistate dynamics to a set of independent
systems of simpler interaction pattern and uncoupled spectator states. The
standard MS transformation imposes restrictions on the time dependence of the
external fields addressing the states, as it requires that both Rabi
frequencies have the same time profile. In this work we treat the case of the
time-dependent MS transformation, which opens prospects for a variety of
physically interesting processes wherein the fields may have different time
dependences. We explore the adiabatic and the double-adiabatic limit, in which
we demonstrate population transfer between the MS states that results in
population transfer from one set of states onto another. We demonstrate the
generation of superposition states between the MS states by the techniques of
half adiabatic passage and fractional stimulated Raman adiabatic passage, which
translate to superpositions of all the states of the involved levels.
