We construct local solutions to eleven-dimensional supergravity describing M2branes intersecting and/or ending on M5-branes, in the near-horizon limit of the M2branes. Global solutions describing these theories should have 16 supercharges and asymptotic AdS 4 × S 7 regions, as well as M5-branes wrapping AdS 3 × S 3 subspaces. We construct the local solution describing a stack of an arbitrary number of M5branes with AdS 3 ×S 3 worldvolume and arbitrary M2-brane charge. Our construction provides a mechanism to get around the no-go theorem that rules out the existence of global solutions preserving 16 supercharges interpolating between AdS 7 × S 4 and AdS 4 × S 7 regions.