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Using a data sample of $e^+e^-$ collision data corresponding to an integratedluminosity of 2.93 $fb^{-1}$ collected with the BESIII detector at acenter-of-mass energy of $\sqrt{s}= 3.773~GeV$,we search for the singlyCabibbo-suppressed decays $D^{0}\to\pi^{0}\pi^{0}\pi^{0}$,$\pi^{0}\pi^{0}\eta$, $\pi^{0}\eta\eta$ and $\eta\eta\eta$ using the double tagmethod. The absolute branching fractions are measured to be$\mathcal{B}(D^{0}\to\pi^{0}\pi^{0}\pi^{0}) = (2.0 \pm 0.4 \pm 0.3)\times10^{-4}$, $\mathcal{B}(D^{0}\to\pi^{0}\pi^{0}\eta) = (3.8 \pm 1.1 \pm0.7)\times 10^{-4}$ and $\mathcal{B}(D^{0}\to\pi^{0}\eta\eta) = (7.3 \pm 1.6\pm 1.5)\times 10^{-4}$ with the statistical significances of $4.8\sigma$,$3.8\sigma$ and $5.5\sigma$, respectively, where the first uncertainties arestatistical and the second ones systematic. No significant signal of$D^{0}\to\eta\eta\eta$ is found, and the upper limit on its decay branchingfraction is set to be $\mathcal{B}(D^{0}\to\eta\eta\eta) < 1.3 \times 10^{-4}$at the $90\%$ confidence level.

Measurement of Singly Cabibbo-Suppressed Decays $D^{0}\to\pi^{0}\pi^{0}\pi^{0}$, $\pi^{0}\pi^{0}\eta$, $\pi^{0}\eta\eta$ and $\eta\eta\eta$