  We continue our study of BPS equations and supersymmetric configurations in
the Bagger-Lambert theory. The superalgebra allows three different types of
central extensions which correspond to compounds of various M-theory objects:
M2-branes, M5-branes, gravity waves and Kaluza-Klein monopoles which intersect
or have overlaps with the M2-branes whose dynamics is given by the
Bagger-Lambert action. As elementary objects they are all 1/2-BPS, and multiple
intersections of $n$-branes generically break the supersymmetry into $1/2^n$,
as it is well known. But a particular composite of M-branes can preserve from
1/16 up to 3/4 of the original ${\cal N}=8$ supersymmetries as previously
discovered. In this paper we provide the M-theory interpretation for various
BPS equations, and also present explicit solutions to some 1/2-BPS equations.
