  Stringent restrictions for model building are imposed by a no-go theorem in
noncommutative gauge field theory. Circumventing this theorem is crucial for
the construction of realistic models of particle interactions. To this end, the
noncommutative construction of tensor representations of gauge groups using
half-infinite Wilson lines is extended to allow for gauge groups consisting of
an arbitrary number of $U_*(N)$ factors. This as well allows representations
other than the ones permitted by the no-go theorem.
