Social choice models usually assume that choice is among pre-defined, uni-dimensional and simple objects. Very often, on the contrary, choice is among multifeatured and complex objects: a candidate in an election stands for an electoral programme which is a complex bundle of many interdependent political positions on a wide variety of issues. Also in committees and organizations of various sorts collective choices are most often made among policy bundles and authorities can act upon the pre-choice stage of construction of such bundles. This pre-choice power of alternatives construction may grant authorities a highly effective device to influence the outcome of social choice even when the latter is totally free and democratic. In this paper we propose a model which investigates within a simple majority vote framework the role of the object construction power, an analogous to the agenda power. Even when object construction is simply defined as the possibility of assembling and dis-assembling a fixed set of choice components into bundles, we show that, under rather general condition, it can radically change the outcome of the majority voting process. In particular we show that any set of bundles (that we call choice modules) is associated to a set of possible social outcomes which can be attained depending upon the initial conditions. Moreover we shows that also Condorcet-Arrow cycles can appear or disappear depending upon which set of modules is chosen.