  In this paper we generalize our previous model (arXiv: 1705.09331), on a
hidden conformal symmetry of smooth braneworld scenarios, to the case with two
real scalar fields non-minimally coupled to gravity. The gauge condition
reduces the action of the system to the action were gravity minimally couples
to one of the scalar fields, plus a cosmological constant. We show that,
depending on the internal symmetry of the scalar fields, the two possibilities,
$SO(2)$ or $SO(1,1)$, emerge. In the $SO(2)$ case we get a ghost-like scalar
field action, which can describe two models -- Standing Wave and Sine-Gordon
smooth braneworlds. For the $SO(1,1)$ case we get the standard sign for the
kinetic part of the scalar field. By breaking the $SO(1,1)$ symmetry (but
keeping the conformal one) we are able to get two Randall-Sundrum models, with
a non-minimal coupling and with a scalar field having hyperbolic potential. We
conclude that this method can be seen as a solution-generating technique and a
natural way to introduce non-trivial scalar fields that can provide smooth
braneworld models.
