A bstract The affine Yangian of gl 1 is isomorphic to the universal enveloping algebra of W 1 + ∞ and can serve as a building block in the construction of new vertex operator algebras. In 1, a two-parameter family generalization of N = 2 supersymmetric W ∞ algebra was constructed by “gluing” two affine Yangians of gl 1 using operators that transform as (□, □ ¯ ) and ( □ ¯ , □) w.r.t. the two affine Yangians. In this paper we realize a similar (but non-isomorphic) two-parameter gluing construction where the gluing operators transform as (□, □) and ( □ ¯ , □ ¯ ) w.r.t. the two affine Yangians. The corresponding representation space consists of pairs of plane partitions connected by a common leg whose cross-section takes the shape of Young diagrams, offering a more transparent geometric picture than the previous construction.