  Magnetic frustration in metallic rare earth lanthanides ($Ln$) with
$4f$-electrons is crucial for producing interesting magnetic phases with high
magnetic anisotropy where intertwined charge and spin degrees of freedom lead
to novel phenomena. Here we report on the magnetic, thermodynamic, and
electrical transport properties of TbAuAl$_4$Ge$_2$. Tb ions form 2-dimensional
triangular lattice layers which stack along the crystalline $c$-axis. The
magnetic phase diagram reveals multiple nearly degenerate ordered states upon
applying field along the magnetically easy $ab$-plane before saturation. The
magnetoresistance in this configuration exhibits intricate field dependence
that closely follows that of the magnetization while the specific heat reveals
a region of highly enhanced entropy, suggesting the possibility of a
non-trivial spin textured phase. For fields applied along the $c$-axis (hard
axis), we find linear magnetoresistance over a wide range of fields. We compare
the magnetic properties and magnetoresistance with an isostructral
GdAuAl$_4$Ge$_2$ single crystals. These results identify TbAuAl$_4$Ge$_2$ as an
environment for complex quantum spin states and pave the way for further
investigations of the broader $Ln$AuAl$_4$Ge$_2$ family of materials.
