  Heavy fermion (HF) materials exhibit a rich array of phenomena due to the
strong Kondo coupling between their localized moments and itinerant electrons.
A central question in their study is to understand the interplay between
magnetic order and charge transport, and its role in stabilizing new quantum
phases of matter. Particularly promising in this regard is a family of
tetragonal intermetallic compounds Ce{$TX$}$_2$ ($T=$ transition metal, $X=$
pnictogen), that includes a variety of HF compounds showing $T$-linear
electronic specific heat $\bf{C_e \sim \gamma T}$, with $\gamma\sim$ 20-500
mJ$\cdot$mol$^{-1}$~K$^{-2}$, reflecting an effective mass enhancement ranging
from small to modest. Here, we study the low-temperature field-tuned phase
diagram of high-quality CeAgBi$_2$ using magnetometry and transport
measurements. We find an antiferromagnetic transition at ${T_{N} = 6.4}$~K with
weak magnetic anisotropy and the easy axis along the $c$-axis, similar to
previous reports (${T_{N} = 6.1}$~K). This scenario, along with the presence of
two anisotropic Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions, leads to a
rich field-tuned magnetic phase diagram, consisting of five metamagnetic
transitions of both first and second order. In addition, we unveil an anomalous
Hall contribution for fields $H<54$ kOe which is drastically altered when $H$
is tuned through a trio of transitions at 57, 78, and 84~kOe, suggesting that
the Fermi surface is reconstructed in a subset of the metamagnetic transitions.
