When the Maplex Label Engine is placing labels, there will always be competition for space. Setting conflict resolution specifications allows you to optimally use the available space for labels to be placed in.
Space can be controlled by setting feature weights, allowing labels to be placed over features if necessary, and setting a label as a background and always allowing other labels to be placed over the top of it. When a label must be placed on the map, you can choose the Never remove (place overlapping) option; the label will be placed regardless of space available, potentially resulting in overlapping labels.