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Dynamic mode decomposition (DMD) provides a principled approach to extract physically interpretable spatial modes from time-resolved flow field data, along with a linear model for how the amplitudes of these modes evolve in time. Recently, DMD has been extended to work with more realistic data that is under-resolved either in time or space, or with data collected in the same spatial domain over multiple independent time windows. In this work, we develop an extension to DMD to synthesize globally consistent modes from velocity fields collected independently in multiple partially overlapping spatial domains. We propose a tractable optimization to identify modes that span multiple windows and align their phases to be consistent in the overlapping regions. First, we demonstrate this approach on data from direct numerical simulation, where it is possible to split the data into overlapping domains and benchmark against ground-truth modes. We consider the laminar flow past a cylinder as an example with distinct frequencies, along with the spatially developing mixing layer, which exhibits a frequency spectrum that evolves continuously as the measurement window moves downstream. Next, we analyze experimental velocity fields from PIV in six overlapping domains in the wake of a cross-flow turbine. On the numerical examples, we demonstrate the robustness of this approach to increasing measurement noise and decreasing size of the overlap regions. In all cases, it is possible to obtain a phase-aligned, composite reconstruction of the full time-resolved flow field from the phase-consistent modes over the entire domain.