  In a recent work we have developed a robust chainwise atom-molecule adiabatic
passage scheme to produce ultracold ground-state molecules via
photo-associating free atoms [J. Qian {\it et.al.} Phys. Rev. A 81 013632
(2010)]. With the help of intermediate auxiliary levels, the pump laser
intensity requested in the atomic photo-association process can be greatly
reduced. In the present work, we extend the scheme to a more generalized
(2$n$+1)-level system and investigate the efficiency limitation for it. As the
increase of intermediate levels and auxiliary lasers, the atom-molecule
adiabatic passage would be gradually closed, leading to a poor transfer
efficiency. For the purpose of enhancing the efficiency, we present various
optimization approaches to the laser parameters, involving order number $n$,
relative strength ratio and absolute strength. We show there can remain a limit
on the population transfer efficiency given by a three-level $\Lambda$ system.
In addition, we illustrate the importance of selecting an appropriate number of
intermediate levels for maintaining a highly efficient transfer under mild
experimental conditions.
