  Reduced general relativity for four-dimensional spherically-symmetric
stationary space-times, more simply called the black hole mini-superspace, was
shown in previous work to admit a symmetry under the three-dimensional
Poincar\'e group ISO(2,1). Such a non-semi-simple symmetry group usually
signals that the system is a special case of a more general model admitting a
semi-simple Lie group symmetry. We explore here possible modifications of the
Hamiltonian constraint of the mini-superspace. We identify in particular a
continuous deformation of the dynamics that lifts the degeneracy of the
Poincar\'e group and leads to a SO(3,1) or SO(2,2) symmetry. This deformation
is not related to the cosmological constant. We show that the deformed dynamics
can be represented as the superposition of two non-interacting homogeneous FRW
cosmologies, with flat slices filled with perfect fluid. The resulting modified
black hole metrics are found to be non-singular.
