The ornamental design for a multi-purpose adjustable retaining device, as shown and described.
FIG. 1 depicts a top plan view of a multi-purpose adjustable retaining device;
FIG. 2 depicts a left side elevation view of the multi-purpose adjustable retaining device;
FIG. 3 depicts a bottom plan view of the multi-purpose adjustable retaining device;
FIG. 4 depicts a right side elevation view of the multi-purpose adjustable retaining device; and,
FIG. 5 depicts a top plan view of the of the multi-purpose adjustable retaining device being utilized with a bed sheet wherein the dashed and dotted lines shown are presented for environmental purposes only and form no part of the claimed design.