  A theory T is tight if different deductively closed extensions of T (in the
same language) cannot be bi-interpretable. Many well-studied foundational
theories are tight, including PA [Visser2006], ZF, Z2, and KM [enayat2017]. In
this article we extend Enayat's investigations to subsystems of these latter
two theories. We prove that restricting the Comprehension schema of Z2 and KM
gives non-tight theories. Specifically, we show that GB and ACA0 each admit
different bi-interpretable extensions, and the same holds for their extensions
by adding Sigma^1_k-Comprehension, for k <= 1. These results provide evidence
that tightness characterizes Z2 and KM in a minimal way.
