Yes, depending on the size of the plant, take cuttings vertically encompassing leaves, central stem and roots in each piece. A vertical division in half is a good way to go. Larger rosettes can be divided in half, then the halves divided again to get quarters. Let dry a couple of days, then plant. Keep on the dry side for a few weeks to let roots develop and the plant start to regenerate.
One thing to keep in mind is that when taking cuttings, expect the plant to use the current growing season to heal and regenerate. Then next growing season (year) you can divide the resulting chicks/rosettes or let grow as a clump. You can even take cuttings again in the second year if necessary, repeating the process.
