  We address the problem of two pairs of fermions living on an arbitrary number
of single particle levels of a potential well (mean field) and interacting
through a pairing force. The associated solutions of the Richardson's equations
are classified in terms of a number $v_l$, which reduces to the seniority $v$
in the limit of large values of the pairing strength $G$ and yields the number
of pairs not developing a collective behaviour, their energy remaining finite
in the $G\to\infty$ limit. We express analytically, through the moments of the
single particle levels distribution, the collective mode energy and the two
critical values $G_{\rm cr}^{+}$ and $G_{\rm cr}^{-}$ of the coupling which can
exist on a single particle level with no pair degeneracy. Notably $G_{\rm
cr}^{+}$ and $G_{\rm cr}^{-}$ merge when the number of single particle levels
goes to infinity, where they coincide with the $G_{\rm cr}$ (when it exists) of
a one pair system, not envisioned by the Richardson theory. In correspondence
of $G_{\rm cr}$ the system undergoes a transition from a mean field to a
pairing dominated regime. We finally explore the behaviour of the excitation
energies, wave functions and pair transfer amplitudes finding out that the
former, for $G>G_{\rm cr}^{-}$, come close to the BCS predictions, whereas the
latter display a divergence at $G_{\rm cr}$, signaling the onset of a long
range off-diagonal order in the system.
