The concept of a hypergeneralized projector as a matrix H satisfying H 2 =H † , where H † denotes the Moore–Penrose inverse of H, was introduced by Groß and Trenkler [Generalized and hypergeneralized projectors, Linear Algebra Appl. 264 (1997) 463–474]. In the present paper, the problem of when a linear combination c 1 H 1 +c 2 H 2 of two hypergeneralized projectors H 1 ,H 2 is also a hypergeneralized projector is considered. Although, a complete solution to this problem remains unknown, this article provides characterizations of situations in which (c 1 H 1 +c 2 H 2 ) 2 =(c 1 H 1 +c 2 H 2 ) † derived under certain commutativity property imposed on matrices H 1 and H 2 . The results obtained substantially generalize those given in the above mentioned paper by Groß and Trenkler.