  We report progress on extending the relativistic model-independent
quantization condition for three particles, derived previously by two of us, to
a broader class of theories, as well as progress on checking the formalism. In
particular, we discuss the extension to include the possibility of 2->3 and
3->2 transitions and the calculation of the finite-volume energy shift of an
Efimov-like three-particle bound state. The latter agrees with the results
obtained previously using non-relativistic quantum mechanics.
