Measurement of Singly Cabibbo-Suppressed Decays $D^{0}topi^{0}pi^{0}pi^{0}$, $pi^{0}pi^{0}eta$, $pi^{0}etaeta$ and $etaetaeta$

Using a data sample of $e^+e^-$ collision data corresponding to an integrated luminosity of 2.93 $fb^{-1}$ collected with the BESIII detector at a center-of-mass energy of $sqrt{s}= 3.773~GeV$,we search for the singly Cabibbo-suppressed decays $D^{0}topi^{0}pi^{0}pi^{0}$, $pi^{0}pi^{0}eta$, $pi^{0}etaeta$ and $etaetaeta$ using the double tag method. The absolute branching fractions are measured to be $mathcal{B}(D^{0}topi^{0}pi^{0}pi^{0}) = (2.0 pm 0.4 pm 0.3)times 10^{-4}$, $mathcal{B}(D^{0}topi^{0}pi^{0}eta) = (3.8 pm 1.1 pm 0.7)times 10^{-4}$ and $mathcal{B}(D^{0}topi^{0}etaeta) = (7.3 pm 1.6 pm 1.5)times 10^{-4}$ with the statistical significances of $4.8sigma$, $3.8sigma$ and $5.5sigma$, respectively, where the first uncertainties are statistical and the second ones systematic. No significant signal of $D^{0}toetaetaeta$ is found, and the upper limit on its decay branching fraction is set to be $mathcal{B}(D^{0}toetaetaeta) < 1.3 times 10^{-4}$ at the $90%$ confidence level.