  We investigate the formation of discs within binary systems where at least
one component has left the main sequence. In particular we calculate the
occurrence rates of systems which can host long-lived, massive discs that may
be able to support the formation of planets. We synthesize a population based
on Milky Way properties, using both theoretical and observational inputs to
constrain key properties such as the shape of the initial mass function, binary
fraction, and mass transfer physics. We predict 0.26\% of binary systems will
host Second generation discs (where the primary has evolved), and 0.13\% of
systems will host Third generation discs (where the secondary also evolves).
For the Milky Way, this translates into 130 million and 90 million Second and
Third generation systems respectively from an estimated total of 50 billion
binary systems. Of these systems that form discs, we estimate approximately
20\% of Second and 3.8\% of Third generation discs have enough mass to form a
planetary system. We speculate on how the process of planet formation differs
in these systems from conventional planet formation in protostellar discs.
