The ornamental design for a suctioncup with handle and base, as shown and described.
FIG. 1 is a perspective view of the suction cup with handle and base showing our new design;
FIG. 2 is a front view thereof;
FIG. 3 is a back view thereof;
FIG. 4 is a side view thereof;
FIG. 5 is an opposite side view thereof;
FIG. 6 is a top view thereof; and,
FIG. 7 is a bottom view thereof.
The broken lines in the drawings showing parts of the suction cup handle and base are for illustrative purposes only and form no part of the claimed design.