  We present Atacama Large Millimeter/submillimeter Array (ALMA) observations
of multiple protostar systems in the Perseus molecular cloud previously
detected by the Karl G. Jansky Very Large Array (VLA). We observed 17 close
($<$600~AU separation) multiple systems at 1.3~mm in continuum and five
molecular lines (i.e., \twco, \cateo, \thco, H$_2$CO, SO) to characterize the
circum-multiple environments in which these systems are forming. We detect at
least one component in the continuum for the 17 multiple systems. In three
systems, one companion is not detected, and for two systems the companions are
unresolved at our observed resolution. We also detect circum-multiple dust
emission toward 8 out of 9 Class 0 multiples. Circum-multiple dust emission is
not detected toward any of the 8 Class I multiples. Twelve systems are detected
in the dense gas tracers toward their disks/inner envelopes. For these 12
systems, we use the dense gas observations to characterize their formation
mechanism. The velocity gradients in the circum-multiple gas are clearly
orthogonal to the outflow directions in 8 out of the 12 systems, consistent
with disk fragmentation. Moreover, only two systems with separations $<$200~AU
are \textit{inconsistent} with disk fragmentation, in addition to the two
widest systems ($>$500~AU). Our results suggest that disk fragmentation via
gravitational instability is an important formation mechanism for close
multiple systems, but further statistics are needed to better determine the
relative fraction formed via this method.
