Muscalu, Tao, and Thiele prove $L^p$ estimates for the "Biest" operator defined on Schwartz functions by the map $$ C^{1,1,1}: (f\_1, f\_2, f\_3) \mapsto \int\_{\xi\_1 < \xi\_2 < \xi\_3} \Big\[ \prod\_{j=1}^3 \hat{f}\_j (\xi\_j) : e^{2 \pi i x \xi\_j } \Big] ,d \vec{\xi} $$ via a time-frequency argument that produces bounds for all multipliers with non-degenerate trilinear simplex symbols. In this article we prove $L^p$ estimates for a pair of simplex multipliers defined on Schwartz functions by the maps \begin{align\*} C^{1,1,-2}:\ & (f\_1, f\_2, f\_3) \mapsto \int\_{\xi\_1 < \xi\_2 < -{\xi\_3}/{2}}\Big\[ \prod\_{j=1}^3 \hat{f}\_j (\xi\_j) \\: e^{2 \pi i x \xi\_j } \Big] \\,d \vec{\xi} \\\ C^{1,1,1,-2}:\ & (f\_1, f\_2, f\_3, f\_4) \mapsto \int\_{\xi\_1 < \xi\_2 < \xi\_3 < -{\xi\_4}/{2}} \Big\[\prod\_{j=1}^4 \hat{f}\_j (\xi\_j) \\: e^{2 \pi i x \xi\_j} \Big] \\,d \vec{\xi} \end{align\*} for which the non-degeneracy condition fails. Our argument combines the standard $\ell^2$-based energy with an $\ell^1$-based energy in order to enable summability over various size parameters. As a consequence, we obtain that $C^{1,1,-2}$ maps into $L^p$ for all $1/2 < p < \infty$ and $C^{1,1,1,-2}$ maps into $L^p$ for all $1/3 < p < \infty$. Both target $L^p$ ranges are shown to be sharp.