  A classification is given for (regular) positions of direct sums of two
matroid algebras (unital algebraic limits of matrix algebras) in a matroid
superalgebra, where the individual summands have index 2 in their associated
corner algebra. A similar classification is obtained for positions of direct
sums of 2-symmetric algebras and, in the odd case, for the positions of sums of
2-symmetric C*-algebras in matroid C*-algebras. The approach relies on an
analysis of intermediate non-self-adjoint operator algebras and the
classifications are given in terms of K0 invariants, partial isometry homology
and scales in the associated composite K0-homology group.
