am working on a project to do country-wide mapping using projected coordinate system such UTM. However, the country (Zambia) is covered by three UTM zones, namely zone 34,35 and 36.I have read literature on possibility of widening UTM zones and the resulting worsening of errors. My concern is on how to modify UTM zones to cover as much as 12 degrees of longitude in one zone. The central meridian will of course be moved to the center.
If your study area covers three UTM zones, just take the middle one to work with.
As you note, the error in the outer parts increases. If this is a major problem for you, think of using a different projection, like Lambert conformal conical or Equal Area. It depends whether you need exact distances, areas or angles. You can minimize distortion on one of these, but not all of them.
UTM is suitable along meridians. For east-west stretching areas, Albers equal-area conic projection is better.