Advice on renegotiating day rates

Hi it's my first post here so go easy on me!

Ok, a little background, I'm currently freelancing for a large international blue chip technology company. I'm contracted in as a "senior designer", via a design agency, through my recruitment agent. It's a little weird in so much as I've never met the design agency let alone worked with them before, but let's move on from that.

I've been there for 20 days now and my contract is being extended until the end of march, perhaps longer. The issue I have is that the longer I'm there the more demanding they're being of me. Essentially I'm going to be the senior art director of the global launch of a new product, and yesterday I received a brief that would more traditionally be given to a creative team. While I don't doubt my ability to fullfil these briefs (in a modest way!) my question to you is should I be renegotiating my day rate? Whilst I'm not unhappy with day rate, I know that if they'd hired an art director or a team they'd be paying more. At the end of the day I'll continue the contract regardless but where do you think I stand with regards to renegotiating my rate, and how should I go about doing it? I know there's two people in the chain who are making their mark up so there must be some room for movement!

Any help would be great.
The chain of people sounds like an issue and seeking to renogiatiate would therefore carry a bit of risk as everyone will want to protect their percentage (and they did source the work for you in the first place, right?). You can try saying you'd like a bit more on the grounds that this is normally the kind of thing that would be handled by a team rather than an individual but the smart answer to that would be that they'd expect to get more from a team. Also, are you working to a fixed fee for this engagement or is it a straight day rate? If the latter, I assume you'll pick up any shortfall in the hours you bill simply by virtue of the fact that you'll be doing more than one person's job...