I think you have to be a little careful here:
So it's typical that they're giving you an offer and a deadline and not the typical when you can start thing? or it is up to software company?
I have to say it is pretty normal - fairly common that, yes, you sometimes have to make an instant decision and instant rate negotiation, and start very soon.
In such a situation, if you say "Oh I have to think about it for seven days" (which is what you're suggesting - until the next Monday at the earliest) - what will happen?
The tycoon in question won't say "well screw you, get lost". She or he will say "Oh .. ok .. fine then" and immediately go off to the next ten meetings of the day.
Over the next seven days there will be a host of people (including me!) desperate to get the project if it's interesting, and indeed, a week is forever in software and Tycoon-land; he or she may have just drifted off to other projects, the whole architecture may have changed or whatever.
I have to say that for "better" jobs or contracts - the really good ones you really want that are really interesting - it is not uncommon you have to make aggressive snap decisions.
Man - there was an interesting question on this site. The person on this list, P, reported that someone telephoned to discuss a job. The person P answered "Oh, I'm driving and I'll call you back". {Driving or similar, I forget.} Of course - they lost the opportunity. The end.
Be cautious.
Actual idea ..
Is there not some way you can get the Friday folks moved forward? (You're so keen right? :) )
Conversely you could put off the first one a few days to make them closer, but who delays interviews?