  Unconventional superconductivity in Sr$_{2}$RuO$_{4}$ has been intensively
studied for decades. The origin and nature of the pairing continues to be
widely debated, in particular, the possibility of a triplet origin of Cooper
pairs. However, complexity of Sr$_{2}$RuO$_{4}$ with multiple low-energy
scales, involving subtle interplay among spin, charge and orbital degrees of
freedom, calls for advanced theoretical approaches which treat on equal footing
all electronic effects. Here we develop a novel approach, a detailed \emph{ab
initio} theory, coupling quasiparticle self-consistent \emph{GW} approximation
with dynamical mean field theory (DMFT), including both local and non-local
correlations. We report that the superconducting instability has multiple
triplet and singlet components. In the unstrained case the triplet eigenvalues
are larger than the singlets. Under uniaxial strain, the triplet eigenvalues
drop rapidly and the singlet components increase. This is concomitant with our
observation of spin and charge fluctuations shifting closer to wave-vectors
favoring singlet pairing in the Brillouin zone. We identify a complex mechanism
where charge fluctuations and spin fluctuations co-operate in the even-parity
channel under strain leading to increment in $T_c$, thus proposing a novel
mechanism for pushing the frontier of $T_c$ in unconventional `triplet'
superconductors.
