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We introduce and study notions of bigraded formality for the algebra of formson a complex manifold, along with their relation to higherAeppli-Bott-Chern-Massey products which extend the case of triple productsstudied by Angella-Tomassini. We show that these Aeppli-Bott-Chern-Masseyproducts on complex manifolds pull back non-trivially to the blow-up along acomplex submanifold, as long their degree is less than the real codimension ofthe submanifold.

Bigraded notions of formality and Aeppli-Bott-Chern-Massey products