'Having designs' is a common phrasing in Chinese novels when translated to English. In them, it's used to signify plans to get them in bed usually. Sometimes also malicious plans.

It's got a bit of everything. Sorry to disappoint, but starting this one gave me motivation to get back into Becoming A Sovereign. So I don't think I'll be updating this for quite some time unfortunately since the plotline for BAS is at least a few hundred chapters.