In recent years we have demonstrated that 2-mm-diameter poly(-methylstyrene) mandrels meeting indirect drive NIF surface symmetry specifications can be produced using microencapsulation methods. Recently higher gain target designs have been introduced that rely on frequency doubled (green) laser energy and require capsules up to 4 mm in diameter, nominally meeting the same surface finish and symmetry requirements as the existing 2-mm-diameter capsule designs. Direct drive on the NIF also requires larger capsules. In order to evaluate whether the current microencapsulation-based mandrel fabrication techniques will adequately scale to these larger capsules, we have explored extending the techniques to 4-mm-diameter capsules. We find that microencapsulated shells meeting NIF symmetry specifications can be produced, the processing changes necessary to accomplish this are presented here.