  The first and second-order supersymmetry transformations can be used to
manipulate one or two energy levels of the initial spectrum when generating new
exactly solvable Hamiltonians from a given initial potential. In this paper, we
will construct the first and second-order supersymmetric partners of the
trigonometric Rosen-Morse potential. Firstly, it is identified a set of
solutions of the initial stationary Schr\"odinger equation which are
appropriate for implementing in a simple way non-singular transformations,
without inducing new singularities in the built potential. Then, the way the
spectral manipulation works is illustrated through several specific examples.
