The complete classification of Wess–Zumino–Novikov–Witten modular invariant partition functions is known for very few affine algebras and levels, the most significant being all levels of A1 and A2 and level 1 of all simple algebras. Here, the classification problem is addressed for the nicest high rank semisimple affine algebras: (A1(1))⊕r. Among other things, all automorphism invariants are found explicitly for all levels k=(k1,...,kr), and the classification for A(1)1⊕A(1)1 is completed for all levels k1, k2. The classification problem for (A1(1))⊕r is also solved for any levels ki with the property that for i ≠ j each gcd(ki+2,kj+2)≤3. In addition, some physical invariants are found which seem to be new. Together with some recent work by Stanev, the classification for all (A1(1))k⊕r could now be within sight.