Cut three pieces of 2-by-4 to 45 inches long for each 4- by 8-foot section of staging you intend to build. You will also need two full-length 2-by-4s.
Place a 4-by-8 foot sheet of ¾-inch plywood on a pair of sawhorses. Align the two full length 2-by-4s on their narrow edge, along both long edges of the plywood. Flush them with the edge and clamp them in place with bar clamps. Drive 1 5/8-inch treated decking screws, one every 10 inches, through the plywood into the edge of the 2-by-4.
Position the three pieces of 2-by-4 you cut perpendicular between the long pieces, one flush at each end and one centered in the middle of the plywood. Stand these 2-by-4s on edge and screw through the long 2-by-4s into their ends with 3-inch treated deck screws. Use two screws in each joint. Drive 1 5/8-inch treated deck screws into each piece through the plywood, as for the long edge pieces. Create as many of these as you need to create the size stage required.
Cut 4 3/4-inch thick plywood pieces for each supporting column. You will need one for each outside corner and one for each corner junction between two or more platforms. Cut 2 pieces 24 by 12 inches and two 24 by 10 1/2 inches, for each column.
Cut a notch in the center of one narrow end of each column piece, 3 inches wide and 3 1/2 inches tall. The notch should be situated flush with the narrow end of the piece, so that one 3-inch side is open to the top.
Stand one 12-inch wide and one 10 ½-inch wide piece on their narrow ends. Glue along one long edge of the 10 ½-inch piece. Match up the edges of the two pieces, so that the 12-inch piece overlaps the 10 ½-inch piece and is flush along its edge.
Nail through the 12-inch piece into the edge of the 10 ½-inch piece with a pneumatic pin nailer, and 1 ½-inch nails, six nails in each joint. Repeat this process to assemble the other half of the first column.
Glue and nail the two halves of the column together to form an open ended box 24 inches high, by 12 inches wide. Build as many of these columns as you need. Fit the platforms together using the notches in the columns to cradle the frames of 2 adjoining platforms, pulling them together. A single platform can hold the intersection between four platforms, with each nesting one corner into the notches to form a T. Support outside corners with a column under the platform, inside the 2-by-4 frame.