Group Multi Picker Only allows for Single Pick on Filter

Currently, when I select a Multi Group Picker custom field, the only option for the search template is to select a single group. Seems like I should be able to select multiple groups on the filter as well. Ideally, i would like to make the assigning function a single select and the filter a multi-select.

The idea is this. A user may be a member of multiple groups. We don't use the assign to feature that often because we may have 15 people in a group and any one of them may handle the issue. This also helps us keep the load evenly distributed as assigning every ticket may overload a particular person. If I assign a ticket to a group using the group picker, I would like to be able to select multiple groups in the filter.