  In a previous work, we noted that vacua with higher flux could be obtained by
recombination of a small set of hidden-sector branes, numbering up to the
Kahler degrees of freedom left to be fixed in the problem. Here, we discuss the
general construction of Type IIB Standard Model flux vacua in which multiple
branes participate in brane recombination in the hidden sector. We present
several models with 4, 5 and 10 branes in a stack. They are complete with
Pati-Salam gauge group, Standard Model chiral matter, and a hidden sector that
combines with nonzero flux to satisfy RR tadpole constraints. We also
illustrate a puzzle: within the 4-brane recombination approach, we are unable
to find a formal cutoff on the number of Standard Model flux vacua.
Nevertheless, we show that phenomenological considerations are sure to cut off
the number of vacua, albeit at an extraordinarily large value. We comment on
the possibility that more formal constraints could further reduce the number of
vacua.
