Triple collocation is an established technique for retrieving linear calibration coefficients and observation error variances of a physical quantity observed simultaneously by three different observation systems. The formalism is extended to an arbitrary number of systems, and representativeness errors and associated cross-covariances are included in a natural way. It is applied to quadruple collocations of ocean surface vector winds from two scatterometers (ASCAT-A, ASCAT-B, or ScatSat), buoy measurements, and NWP model forecasts. There are fifteen possible sets of quadruple collocation equations, twelve of which are solvable for the essential variables (calibration coefficients, observation error variances, and common variance) as well as two additional error covariances, each set leading to a different solution. A remarkable property of the quadruple collocation equations is proven: when the two additional error covariances from a particular solution are used to correct the corresponding observed covariances, all sets yield the same solution. Therefore the quadruple collocation equations by themselves give no information on the representativeness errors involved; these have to be estimated using other methods. The spreading in the solutions is a measure of the accuracy of the underlying error model. Variation of the scale at which the spatial variances are evaluated yields an optimal scale of 100 to 200 km. For the datasets used in this study the error in the scatterometer error variances is 0.03 to 0.05 ms^-1, more than expected on statistical grounds. A more precise determination requires an error model better describing the data.