We develop an approach to subspace system identification using multiple data records and present a simple rank-based test for the adequacy of these data for fitting the unique linear, noise-free, dynamic model of prescribed state-vector, input-vector and output-vector dimensions. The approach is motivated by the prospect of sorting through archives of operational data and extracting a sequence of not-necessarily-contiguous data records individually insufficient for providing identifiability but collectively making this possible. The test of identifiability then becomes the sorting criterion for accepting or rejecting new data records. En passant, the familiar Hankel structure of the data matrices of subspace system identification is reinterpreted and revised.