  We give improved multi-pass streaming algorithms for the problem of
maximizing a monotone or arbitrary non-negative submodular function subject to
a general $p$-matchoid constraint in the model in which elements of the ground
set arrive one at a time in a stream. The family of constraints we consider
generalizes both the intersection of $p$ arbitrary matroid constraints and
$p$-uniform hypergraph matching. For monotone submodular functions, our
algorithm attains a guarantee of $p+1+\varepsilon$ using
$O(p/\varepsilon)$-passes and requires storing only $O(k)$ elements, where $k$
is the maximum size of feasible solution. This immediately gives an
$O(1/\varepsilon)$-pass $(2+\varepsilon)$-approximation algorithms for monotone
submodular maximization in a matroid and $(3+\varepsilon)$-approximation for
monotone submodular matching. Our algorithm is oblivious to the choice
$\varepsilon$ and can be stopped after any number of passes, delivering the
appropriate guarantee. We extend our techniques to obtain the first multi-pass
streaming algorithm for general, non-negative submodular functions subject to a
$p$-matchoid constraint with a number of passes independent of the size of the
ground set and $k$. We show that a randomized $O(p/\varepsilon)$-pass algorithm
storing $O(p^3k\log(k)/\varepsilon^3)$ elements gives a
$(p+1+\bar{\gamma}+O(\varepsilon))$-approximation, where $\bar{gamma}$ is the
guarantee of the best-known offline algorithm for the same problem.
