This talk reports on joint work with Maria Bertozzi, Tara Holm, Emily Maw, Grace Mwakyoma, Ana Rita Pires, and Morgan Weiler on a WiSCon project to investigate the embedding capacity function of the one-point blow up of $\mathbb CP^2$. We found three new families of staircases, that are related by symmetries and have other interesting structural features. This talk will explain our findings and our conjectures.