Maintaining http request in jmeter for certain amo

I want to stimulate say 1000+ users logging in/do stuff/etc and staying in the system, for say 5 minute before logging out/doing something else. While these 1000+ are staying, I will loop it through so additional 1000+ users are sent in and so on - sort of like trying to cram as many users onto the server as possible and keeping them there while cramming more.

Is it possible to do something like this?

I did some looking around, and there is a keepalive option in jmeter, but how long does this last? There is no option to input how long I want it. Also, for the time delay (e.g constant timer), I don't think that'll work for what I'm trying to do right? Since that just delays when the next one starts, without keeping the first alive (or am I misunderstanding it's use?)

I would start saying that "one user = one thread". At the beginning of the design, this assumption help simplify things (you can change later, is you have a very high amount of users). So, your requirement turns into "I want to add as many threads as possible". You can do that using rampup time (standard threads controller", or using some controller from Jmeter-plugins- I found these last ones very useful.

About keep alive option, AFAIK this is only for http sessions control, at low level. I think you need to make each user iterate the script multiple times, (this means each user does login multiple times), OR you can insert some loop inside the script, holding some operation that is done often, OR you can play with timers, making each thread play more slowly. In the end, it depends very much on your requirement, that in turn depends on Application & user behviour.