The time-dependent dynamics of domains formed in Lipid monolayers has been investigated in the case of coexisting lipid phases of different molecular areas. In general, an applied nonequilibrium pressure gives rise to both size and shape changes of domains. In this work, it is shown how the two effects can be superposed, leading to transitions from circular domains to other shapes (such as harmonic modes n = 2, 3, 4...) depending on the value of the applied excess pressure. As the excess pressure changes, the symmetry numbers of the transitions change. The description of the transient states for the growth of circular domains allows one to predict the time for the appearance of the different n-fold distortions. It is shown how in principle a sequence of applied pressures can be used to produce domains with shapes derived from a given distortion symmetry, such as n = 2.