  We push further the study of lineability properties related to sets from
norm-attaining theory. As a matter of fact, we provide several results in the
context of lineability, spaceability, maximal-spaceability, and $(\alpha,
\beta)$-spaceability for sets of non-norm-attaining bounded linear operators
whenever such sets are non-empty. Our results concerning the cardinality of the
linear subspaces are presented in a more general framework, where classical
spaces of bounded linear operators between Banach spaces and their subsets are
considered as special cases. This leads to new results and generalizes several
ones from the literature.
