More than twenty years ago Eugene Tyrtyshnikov discussed with the fourth author the idea of “an extradimensional approach” for treating the singular value distribution and the eigenvalue distribution in the Weyl sense of general matrix-sequences. The idea is indeed fruitful and it has been already exploited in few contexts. In the current note we give account of it by presenting new general tools, with application to the case of \(2\times 2\) block Toeplitz matrix-sequences with potentially rectangular blocks. At the end we present a conjecture and few numerical experiments validating the statement and connected with the general results.