I built the first sets of step stools using the same style as most of my furniture.   Then I thought this is a good place to try some different style ideas.   I had always (for step stools anyway) use 1x3s for the frame but I got to thinking I might make square frame pieces so I thought about trying 1-1/2" X 1-1/2" verticals and horizontals.   Then another thought occurred to me, the chair back would be more comfortable if I kept the 1x3 verticals in the back and all the rest of the frame is 1-1/2 X 1-1/2.

The frame's front will be 2 x 2s (1-1/2" X 1-1/2" square) with 11/16" thick seat, back verticals, back, steps, and seat.   The width and length will be 15" instead of 16".   All joints will be mortis and tenon, the frame of 2x2 tenons will be 1" square and 1/2" long, while all tenons in 11/16 thick material (back and steps) will have 1/2" wide end shoulders with 1/8" on the long side.