Recently, Altavista, Anastasi, Angius and Uranga discussed a method to construct junctions and bouquets of different perturbative string theories. Following this analysis, we here argue that three non-tachyonic ten-dimensional heterotic string theories can be joined together at a nine-dimensional junction. This is done by creating a two-dimensional non-conformal N=(0,1) supersymmetric quantum field theory with three asymptotic ends, each equipped with one of the worldsheet theories of the supersymmetric E₈× E₈ theory, the supersymmetric SO(32) theory, and the non-supersymmetric SO(16)× SO(16) theory, respectively. It is actually a special case of a more general construction involving an arbitrary Z₂-symmetric theory T, its Z₂-orbifold T/Z₂, and the modified Z₂-orbifold (T× q)/Z₂, where q is a certain Z₂-symmetric spin invertible theory.