Bluffing is hard. There's nothing worse than looking some prospective employer in the eye and telling a whopper about other offers. Makes you feel dirty and makes you feel like you can't afford to ask for even more. At the same time you feel like an idiot just taking someone's first offer ...
Therefore,
Go after more than one offer at a time. Don't just show up for the other interviews - go for the gusto and get those other offers. Tell the first offers you have just a few more interviews to do before you can tell them whether you'll accept. Make them feel good about it - tell them you're almost certain to accept, but you want to be fair-minded. If you have to, invoke the AbsentProxy. But don't do anything until you've got at least two offers.
Now pick a remuneration that isn't too far above the market and tell each party that that's what you're talking about with the others. You pretty much know which one you really want, but treat each of them fairly and see how high they'll go - even if you don't go to the top bidder, which if you have any sense you won't do (DontGoToTheHighestBidder), you'll learn a lot about what the market will bear.
When one makes a firm offer, let the others know that this is what you've got so far. Be honest, but manage the information sensibly. See where they all go, then pick the one that suits you best. And use what you learn about the market the next time.
Don't stop doing interviews seriously, ever for a couple weeks after you start the new job because the job may fall through due to budget changes, or there was a reorganization, or it turns out you don't really fit well with the job, or whatever. Sometimes, it really is just too good to be true, so be careful. -- SunirShah
Some of this stuff strikes me as bizarre. A few days after starting work, you ask for an afternoon off so you can interview for a different new job? If I were the employer I would take a very dim view of it.
As for Now pick a remuneration that isn't too far above the market and tell each party that that's what you're talking about with the others. - to me that is edging over the line into dishonesty. You are trying to give the impression that the other parties are comfortable with that over-priced salary. Maybe you can do it without saying an outright lie, but your intention is to deceive. -- DaveHarris
On what Sunir suggests, I don't think I can support doing interviews after you're already committed full time unless a decent interval has passed and you've decided to go looking for the next job. Finding you've been misled about a position and then going to do some interviews, or resuming negotiations with one of your other contacts - well, that seems fair after being misled, don't you think? --PeterMerel.
When I said that you should keep doing interviews even after you've gotten a job/placement, I was inspired by my roommate who on two separate occasions was offered a job, showed up and discovered to his horror that they lied on the job description. He just left. If you've already formally rejected other job offers, you're toast. Perhaps you shouldn't interview directly, but you should still keep an open relationship with all offers until you're sure you're going to stay. -- SunirShah
I used to hate recruitment agencies. I sensed very little respect from them. Now, for some reason (Has the profession grown up? Is it a matter of Internet market vs. where I worked before? Have I changed, myself? I suspect the answer is that I'm now a scarce resource on a high demand market...) I find they make things a lot smoother, as opposed to the approach I previously favored of meeting employers directly. They will contact you discreetly; they know you won't be able to talk much if they catch you during office hours and offer to call in the evenings. If you accept one job, they won't consider the relationship terminated; they will suggest you get in touch at a later date if you ever want a change. I now see them as a good way to ensure I'll have fallback positions. -- LaurentBossavit
Returning to a former company seems to be a very strange situation to me unless you mean with former managers/collegues who've also moved on.
As for holding open multiple offers, I've found most companies want a quick decision and if you don't accept within 24 hours or so they more move onto their second choice.
Part of the NegotiatingPatternLanguage.