When measuring the joint effect of two factors it is advantageous to use a factorial design. If the application is suitable, efficiency may be further improved by using a crossover design. This paper presents a flexible method for amalgamating these two devices. Designs are constructed from smaller designs, known as bricks, generated cyclically from tabulated initial sequences. The bricks have known efficiencies for estimation of direct treatment main effects and interactions; the efficiencies can be simply combined to approximate the efficiencies of the whole design. This allows the user to build a design that is tailored to the particular objectives of the experiment. Three and four periods, and two factors with up to four levels are considered.