Masterton (the guy in Oxford) needs to know if you're reliable. That's why he wants you to invest some time in getting recommendations from other employers. In other words, what you need to do is complete the mission sets from three other people, and then come back to him.
Yes, you can work for two or more people at the same time. However, it's kinda pointless, because if you're trying to do two missions at once, you'll end up failing one (because you generally don't have enough fuel to complete all those jumps). Note that what Masterton tells you to do isn't a mission, though. His mission set is now finished. So get out there, and complete the mission sets for three other people. And if you run into someone while doing a mission for someone else, don't even bother talking to them - just write down where you met them, and get on with the game. Also, keep in mind that some people will tell you about a bounty on someone's head. This is not a mission, but you should write it down - because later on, you end up killing the guy anyway, so you'll want to know where to collect your reward... actually, rewards.
. The difference between the floppy and CD-ROM version is that the floppy has separate exe files for both, while the CD-ROM version only has one exe file.