  We utilize the technique of staircases and jagged partitions to provide
analytic sum-sides to some old and new partition identities of Rogers-Ramanujan
type. Firstly, we conjecture a class of new partition identities related to the
principally specialized characters of certain level $2$ modules for the affine
Lie algebra $A_9^{(2)}$. Secondly, we provide analytic sum-sides to some
earlier conjectures of the authors. Next, we use these analytic sum-sides to
discover a number of further generalizations. Lastly, we apply this technique
to the well-known Capparelli identities and present analytic sum-sides which we
believe to be new. All of the new conjectures presented in this article are
supported by a strong mathematical evidence.
