Yes you can schedule whole families in a single position by turning on the "Never split up family members in this job" option for the job of the position. This feature is often used to schedule one family per shift  as opposed to always scheduling a fixed number of positions.

1. First, select the appropriate job in the Jobs pane and choose to edit the job. In the desktop software this is done by clicking the "Edit Job..." button, and in the Admin view of the Web Terminal this is done by clicking on the pencil icon.

2. Click on the "Show more options for this job..." link

3. Check the "Never split up family members in this job" box and then click OK.

4. Then, in the Recurring Shifts pane you will want to require just one (1) volunteer for each service.

Even though you only require one volunteer, VSP will automatically overload the position with all volunteers that are qualified for the position in one family.