Since we always recommended using set screws (the longest set screws we've found are 4 inches long) and they do penetrate the bracket by about ¾ of an inch, we suggest that when using the aluminum bracket, the maximum thickness generally cannot exceed 5 ½ inches. With that being said, the thickest we generally recommend is around 3" tall unless you want to switch to the steel bracket.
When using the steel bracket we can go much thicker, since the steel bracket comes in different sizes. Starting at 2 ½ inches high and increasing all the way up to 7 inches high in ½ inch increments. A 7-inch steel bracket could do a 9 inch thick shelf.
That said, if we go any higher, one needs to use thicker steel (more than 10 gauge). This becomes very expensive and will always be a custom order.
That aside, in theory, there is no height limit in steel.