Identifying and characterizing systems with coupled and competing interactions is central to the development of physical models that can accurately describe and predict emergent behavior in condensed matter systems. This work demonstrates that the metallic compound CuFe$_2$Ge$_2$ has competing magnetic ground states, which are shown to be strongly coupled to the lattice and easily manipulated using temperature and applied magnetic fields. Temperature-dependent magnetization $M$ measurements reveal a ferromagnetic-like onset at 228(1)\,K and a broad maximum in $M$ near 180\,K. Powder neutron diffraction confirms antiferromagnetic ordering below $T_{\textrm{N}}≈$175\,K, and an incommensurate spin density wave is observed below $≈$125\,K. Coupled with the small refined moments (0.5-1\,$μ_B$/Fe), this provides a picture of itinerant magnetism in CuFe$_2$Ge$_2$. The neutron diffraction data also reveal a coexistence of two magnetic phases that further highlights the near-degeneracy of various magnetic states. These results demonstrate that the ground state in CuFe$_2$Ge$_2$ can be easily manipulated by external forces, making it of particular interest for doping, pressure, and further theoretical studies. ; Comment: Combines main article and supplemental information