  We provide a closed Poisson algebra involving the Ragnisco--Bruschi
generalization of peakon dynamics in the Camassa--Holm shallow-water equation.
This algebra is generated by three independent matrices. From this
presentation, we propose a one-parameter integrable extension of their
structure. It leads to a new $N$-body peakon solution to the Camassa--Holm
shallow-water equation depending on two parameters.
  We present two explicit constructions of a (non-dynamical) $r$-matrix
formulation for this new Poisson algebra. The first one relies on a
tensorization of the $N$-dimensional auxiliary space by a 4-dimensional space.
We identify a family of Poisson commuting quantities in this framework,
including the original ones. This leads us to constructing a second formulation
identified as a spectral parameter representation.
