I just read your post again and might have missed your original meaning.
You can create a data table with columns for the factors and rows with the allowed combinations. Then start Custom Design, change Add N Factors to 4, click Add Factor, and select Covariate. This way, JMP will use the given levels. The levels / combinations are fixed so the custom design can't use the coordinate exchange algorithm in the usual way to generate a design. It will pick a design.
Note that you only need to include the factors with the constraints . You can add independent factors in the usual manner, e.g., as a continuous factor.
Note that you cannot make a design with more runs than the number of rows in this table. If you want a design with more rows, then duplicate the rows in the data table or create new combinations first. If you want fewer runs than the number of rows in the data table, then JMP will select the best subset from the data table.