The ornamental design for a base-mounted multi-pack container holder, as shown and described.
FIG. 1 is a top left perspective view of a base-mounted multi-pack container holder showing my new design.
FIG. 2 is a bottom left perspective view thereof.
FIG. 3 is a front view thereof.
FIG. 4 is a right side view thereof, the left side view being a mirror image of the right.
FIG. 5 is a bottom view thereof; and,
FIG. 6 is a top view thereof.
The dashed lines in FIG. 4 illustrate a bottle inserted at its base into the base-mounted multi-pack container holder of FIG. 1, and form no part of the claimed design.