  We consider heterotic string theories compactified on a K3 surface which lead
to an unbroken perturbative gauge group of Spin(32)/Z2. All solutions obtained
are combinations of two types of point-like instanton --- one ``simple type''
as discovered by Witten and a new type associated to the ``generalized second
Stiefel-Whitney class'' as introduced by Berkooz et al. The new type of
instanton is associated to an enhancement of the gauge symmetry by Sp(4) and
the addition of a massless tensor supermultiplet. It is shown that if four
simple instantons coalesce at an orbifold point in the K3 surface then a
massless tensor field appears which may be used to interpolate between the two
types of instanton. By allowing various combinations of point-like instantons
to coalesce, large gauge groups (e.g., rank 128) with many massless tensor
supermultiplets result. The analysis is done in terms of F-theory.
