Most of negotiation is just asking questions about the other side's needs and constraints, and articulating yours. Often you can find a creative way to solve everyone's needs.
For example, in your case you should find out why they need an answer next week.
If they have a rule that offers can only be open for 7 days, you could ask them to issue the offer later after you've gone through your interview process.
Or if they have backup candidates they might need to engage, let them engage those guys, and you sync up again once your interviews are done.
And you should articulate your constraint: you have an interview "process" that continues for the next xx weeks, after which you can make a well-informed decision. You can also tell them it's in their interest for you to make a well-informed decision - they want someone who chose to work there for the right reasons and will be a long-term, productive employee. Turnover kills companies.
I wouldn't accept an offer unless you really intend to work there. One day you'll be a manager or director, and the karma will come back to bite you :) You always want to be a class act, even when confronted with someone less-than-classy.
If they're reasonable people and they want you, there's probably a good reason for their constraints, and they should be willing to find a solution that fits your constraints too.
If they're not reasonable people, or they don't want you, better to find out now.