  The stransverse mass variable $M_{T2}$ was originally proposed for the study
of hadron collider events in which $N=2$ parent particles are produced and then
decay semi-invisibly. Here we consider the generalization to the case of $N\ge
3$ semi-invisibly decaying parent particles. We introduce the corresponding
class of kinematic variables $M_{TN}$ and illustrate their mathematical
properties. Many of the celebrated features of the $M_{T2}$ kinematic endpoint
are retained in this more general case, including the ability to measure the
mass of the invisible daughter particle from the stransverse mass kink. We
describe and validate a numerical procedure for computing $M_{TN}$ in practice.
We also identify the configurations of visible momenta which result in
nontrivial ($M_{TN}\ne 0$) values, and derive a pure phase-space estimate for
the fraction of such events for any $N$.
