Systems of integral equations are proposed which generalise those prev
iously encountered in connection with the so-called staircase models.
Under the assumption that these equations describe the finite-size eff
ects of relativistic field theories via the thermodynamic Bethe ansatz
, analytical and numerical evidence is given for the existence of a va
riety of new roaming renormalisation group trajectories. For each posi
tive integer k and s = 0,..., k - 1, there is a one-parameter family o
f trajectories, passing close by the coset conformal field theories G(
k) X G(nk+s)/G((n+1)k+s) before finally flowing to a massive theory fo
r s = 0, or to another coset model for s not-equal 0.