  We investigated the evolution of the temperature-composition phase diagram of
Fe$_{1+y}$Te upon Se substitution. In particular, the effect of Se substitution
on the two-step, coupled magneto-structural transition in Fe$_{1+y}$Te single
crystals is investigated. To this end, the nominal Fe excess was kept at $y$ =
0.12. For low Se concentrations, the two magneto-structural transitions
displayed a tendency to merge. In spite of the high Fe-content,
superconductivity emerges for Se concentrations, $x \geq$ 0.1. We present a
temperature-composition phase diagram to demonstrate the interplay of
structure, magnetism, and superconductivity in these ternary Fe chalcogenides.
