Applied at well-known company for Unknown

I reached out to a recruiter I had previously worked with at a well-known company. Earlier this year, I applied for a coordinator role but was rejected. Recently, I got back in touch regarding a lower-level position, which I also didn't get. Now, I've seen another job opening at the same company that I'm really interested in. I'm considering sending a direct email to the recruiter with my updated resume and cover letter. I want to know if this is a good idea or if it might come off as annoying since I've already applied for a couple of roles and faced rejections. I believe my skills align with the positions, and I've made it through mid-stages in the past, so I'm not completely out of the running. I genuinely want to pursue this opportunity but I'm worried about overstepping. Any thoughts?