We have studied the multipolarites of several transitions in the nucleus $^{176}$Lu. The synthesis of $^{176}$Lu in stellar environments is through the slow (s-) neutron capture process. The s-process is responsible for the creation of 50\% of the heavy elements and 15-20 nuclei in the s-process are s-process branching points. Branching points determine if the synthesis path will $eta$-decay or neutron capture. The branching point $^{176}$Lu is only produced via the s-process only and has both a long-lived ground state ($K=7^{-}$) of 37.6 Gy and a short-lived isomeric state ($K=0^{-}$) at 3.6 h. There is no direct decay to both the isomer and ground state due to selection rules. However, an intermediate state was found at 839 keV in the $K=4^{-}$ band and another intermediate state in the $K=4^{+}$ band at 709 keV which communicate to both the isomer and ground state. The communication to both the isomer and ground state through the intermediate states affects the final abundances of $^{176}$Lu in stellar environments which is sensitive to temperature. The experiment was performed at the University of Notre Dame Nuclear Science Laboratory (NSL) using a $^{176}$Yb$(p,n)$ reaction at 7.75 MeV. Gamma-gamma and gamma-electron coincidences were measured for conversion coefficients using the Internal Conversion Electron Ball (ICEBall) array and two HPGe detectors (109\% relative efficiency of a 3'x 3' NaI detector at 1332 keV). ICEBall was upgraded at the NSL for an improved efficiency from 6\%-15\% over $4pi$. A total of 40 conversion coefficients were measured and 35 multipolarities were assigned. 17 new conversion coefficients were measured and the corresponding multipolarities were assigned. Levels and spin assignments in both the $K=4^{+}$ band and $K=4^{-}$ band were verified in the intermediate states that are important for establishing a thermal equilibrium in the s-process.