  Using a renormalization group approach, we determine the phase diagram of an
extended quasi-one-dimensional electron gas model that includes interchain
hopping, nesting deviations and both intrachain and interchain repulsive
interactions. d-wave superconductivity, which dominates over the
spin-density-wave (SDW) phase at large nesting deviations, becomes unstable to
the benefit of a triplet $f$-wave phase for a weak repulsive interchain
backscattering term $g_1^\perp>0$, despite the persistence of dominant SDW
correlations in the normal state. Antiferromagnetism becomes unstable against
the formation of a charge-density-wave state when $g_1^\perp$ exceeds some
critical value. While these features persist when both Umklapp processes and
interchain forward scattering ($g_2^\perp$) are taken into account, the effect
of $g_2^\perp$ alone is found to frustrate nearest-neighbor interchain $d$- and
$f$-wave pairing and instead favor next-nearest-neighbor interchain singlet or
triplet pairing. We argue that the close proximity of SDW and
charge-density-wave phases, singlet d-wave and triplet $f$-wave superconducting
phases in the theoretical phase diagram provides a possible explanation for
recent puzzling experimental findings in the Bechgaard salts, including the
coexistence of SDW and charge-density-wave phases and the possibility of a
triplet pairing in the superconducting phase.
