Overlapping Branes in M-Theory

We construct new supersymmetric solutions of $D$=11 supergravity describing $n$ orthogonally ``overlapping" membranes and fivebranes for $n$=2,3,4. Overlapping branes arise after separating intersecting branes in a direction transverse to all of the branes. The solutions, which generalize known intersecting brane solutions, preserve $2^{-n}$ of the supersymmetry. Each pairwise overlap involves a membrane overlapping a membrane in a 0-brane, a fivebrane overlapping a fivebrane in a 3-brane or a membrane overlapping a a fivebrane in a string. After reducing $n$ overlapping membranes to obtain $n$ overlapping $D$-2branes in $D$=10, $T$-duality generates new overlapping $D$-brane solutions in type IIA and type IIB string theory. Uplifting certain type IIA solutions gives the $D$=11 solutions. Some of the new solutions reduce to dilaton black holes in $D$=4. Additionally, we re-interpret a previously known $D$=10 solution as describing two $D$-5branes overlapping in a string. $T$-duality then generates further $D$=10 solutions and uplifting one of the type IIA solutions gives a new $D$=11 solution describing two fivebranes overlapping in a string.