Consulting Networking 2022 FT

So some questions that might seem a little simple but I'm still kinda unsure about some stuff. When networking say I get a meeting with an analyst who has worked at a firm (MBB,Big 4 etc.) and I charm them what do I do then in the sense of who do I ask to talk to? Do I ask them to give a couple names to message on LinkedIn or ask them to connect me with their manager, other members of their team? Should I try and climb the ladder with these analysts or is there also some worth in messaging managers and higher levels myself? I was also curious whether its worth it to message recruiters rather than actual consultants?