I'm currently looking for my first job after my university education, so I am not that experienced with the application processes of various companies and their schedules.
A few months ago the reply rate to my applications seemed rather low, now a bunch of companies get back to me. I presume that during the summer holiday a large fraction of the HR teams have been on vacation and therefore applications have piled up. Now I am in multiple application processes in parallel and they progress at different speeds.
Say I am in the second round with company A and it feels really great. I work on a project that is to be discussed on the second interview. An appointment for that has yet to be scheduled. There will be third interview with the senior management after that. Then there is company B, C and D, where I will have the next round next week. And then there is company E where I will have the first interview soon.
It will likely take a several weeks until I will get a written offer from any of these. And as I want to start a job eventually, I would try to ask for a little more consideration time, but would have to accept or decline an offer at some point. I would really like to have the offer of the companies in the order of my personal ranking, but that likely won't happen by itself. So I would like to inform the HR of my current favorite company of the situation and ask to already schedule the next round as early as possible to let them be the first to give an offer (if they want).
Now I have tried to express this, but there are two things that always creep in and that I don't want to convey:
Saying that I am interviewing with other companies and that they might make an offer sounds like a threat. Basically I am blackmailing company A to either send me an offer quickly or I might be gone. Surely I will not wait forever, but I am willing to ask the other companies for more consideration time to let company A come to a conclusion. But I also would not want to decline written offers by other companies just on the basis of hope that company A will eventually hire me.
Trying to downplay the time constraints that I would definitely decline all other offers until company A decides is neither completely true, nor does it sound sensible. During the past months I became aware of my skills, and what open positions I get interviewed for. I do really like company A, and would be most happy to work for them. The other companies have interesting work as well, and I don't to make it look like as if I could either become an astronaut with company A or just get hired for a boring job with the other companies.
I presume that HR people know about this scenario with applicants and that I don't have to write much. How could I politely ask for them to schedule the next round already, without blackmail or desperate connotations?