  The tail behavior of aggregates of heavy-tailed random vectors is known to be
determined by the so-called principle of "one large jump'', be it for finite
sums, random sums, or, L\'evy processes. We establish that, in fact, a more
general principle is at play. Assuming that the random vectors are multivariate
regularly varying on various subcones of the positive quadrant, first we show
that their aggregates are also multivariate regularly varying on these
subcones. This allows us to approximate certain tail probabilities which were
rendered asymptotically negligible under classical regular variation, despite
the "one large jump'' asymptotics. We also discover that depending on the
structure of the tail event of concern, the tail behavior of the aggregates may
be characterized by more than a single large jump. Eventually, we illustrate a
similar phenomenon for multivariate regularly varying L\'evy processes,
establishing as well a relationship between multivariate regular variation of a
L\'evy process and multivariate regular variation of its L\'evy measure on
different subcones.
