Can a plan be built with 2x6 framing instead of 2x4 framing?
Almost certainly yes. Some measurements may have to be shifted slightly to accommodate the thicker walls, so you will need to have the designer review the plans and make any necessary changes. The cost will depend on the individual plan but it should be relatively modest. Also, 2X6 framing does increase your material costs and labor somewhat, so you will probably want to 2X6 frame only the exterior walls.