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In this paper, we investigate what selection principles properties are possessed by small (with respect to the bounding and dominating numbers) unions of spaces with certain (star) selection principles. . Furthermore, we give several results about iterations of these properties and weaker properties than paracompactness. In addition, we study the behaviour of these iterated properties on -spaces. Finally, we show that, consistently, there is a normal star-Menger space that is not strongly star-Menger; this example answers a couple of questions posed in J. Casas-de la Rosa, S. A. Garcia-Balan, P. J. Szeptycki, Some star and strongly star selection principles, Topology Appl. 258 (2019) 572-587
Rosa et al. (Sun,) studied this question.