You can create an expression to have labels fit within region boundaries by having them display on multiple lines (so that they wrap from one line to the next within a region boundary). To do this, you would follow the instructions under Labeling with Expressions and add a carriage return to the abbreviation expression.
As an example, you have a layer of capital cities that you want to label on the map, and you want to include the country name in the labels, such as "London, England". Your label expression would look like this:
Capital + ", " + Country
Where Capital and Country are columns in the layer table. This displays on the map as:
London, England
Madrid, Spain
Paris, France
However, some labels may be too long to fit within their regions and do not display as a result. To increase the number of region labels, you can specify an abbreviation expression that includes a carriage return in the middle.
Capital + ", " + Chr$(10) + Country
If the following label does not fit within its country boundary,
London, England
Then it displays as:
London,
England