  We study several cases of IR enhancements of global symmetry in four
dimensions. In particular, we consider a sequence of $Spin(n+4)$ supersymmetric
gauge theories ($8\geq n\geq 1$) with $n$ vectors and spinor matter with $32$
components. We show that the subgroup of the flavor symmetry of these theories
rotating the matter in the spinor representations in the UV, when proper gauge
singlet fields are added, enhances to the commutant of $SU(2)$ in $E_{9-n}$. We
discuss several other interesting cases of enhanced symmetries and the
interplay between symmetry enhancement and self-duality. We also make some
observations about possible interconnections between chiral ring relations and
symmetry enhancement. Finally, we conjecture relations of the discussed models
to compactifications of certain conformal matter models in six dimensions on
tori. The conjecture is based on deriving a relation between five dimensional
models with $Spin$ gauge groups and conformal theories in six dimensions. As a
by product of our considerations we discover a new instance of a simple
self-duality of a theory with an $SU(6)$ gauge group.
