In a large number of applications, including communica- tions from satellites, an optimal exploitation of the available power is of the outmost importance. As a consequence, isophoric array archi- tectures, i.e., arrays using the same power in all the difierent entry points and achieving the ampliflers' maximum e-ciency, are of great interest. At the same time, the easy reconflgurability of the power patterns results fundamental in order to get a full exploitation of the payload. In this paper, an innovative and deterministic approach is proposed for the optimal synthesis of linear phase-only reconflgurable isophoric sparse arrays able to commute their pattern amongst an arbi- trary number of radiation modalities. The introduced perspective leads to an efiective solution procedure for the fast design of antennas with high performance, and does not recur to computationally expensive global-optimization techniques. Numerical results concerning applica- tions of actual interest and employing realistic element patterns are provided in support of the given theory.