One of the scaling factors called out in the Software Development Context Framework (SDCF) is domain complexity.  The general idea is that agile teams will find themselves in different situations where some teams are developing fairly straightforward solutions, such as an informational website, whereas others are addressing very complex domains, such as building an air-traffic control system (ATCS).  Clearly the team building an ATCS will work in a more sophisticated manner than the one building an informational website.  I don't know whether agile techniques have been applied in the development of an ATCS, although I have to think that agile's greater focus on quality and working collaboratively with stakeholders would be very attractive to ATCS delivery teams, I do know that agile is being applied in other complex environments: The 2009 Agility at Scale Survey found that 18% of respondents indicated that their organizations had success at what they perceived to be very complex problem domains,.

Increased domain complexity may affect your strategy in the following ways:

1. Reaching initial stakeholder consensus becomes difficult.  One of the risk reduction techniques called out in Disciplined Agile Delivery (DAD) is to come to (sufficient) stakeholder consensus at the beginning of the project during the Inception phase (called Sprint 0 in Scrum or Iteration 0 in other agile methods).  Stakeholder consensus, or perhaps "near concensus" or "reasonable agreement" are better terms, can be difficult to come to the more complex the problem domain is because the stakeholders may not fully understand the implications of what they're making decisions about and because there is likely a greater range of stakeholders with differing goals and opinions.  The implication is that your project initiation efforts may stretch out, increasing the chance that you'll fall back on the old habits of big requirements up front (BRUF) and incur the costs and risks associated with doing so. 
2. Increased prototyping during inception.   It is very common for disciplined agile teams to do some light-weight requirements envisioning during inception to identify the scope of what they're doing and to help come to stakeholder consensus.  The greater the complexity of the domain, and particularly the less your team understands about the domain, the more likely it is that you'll benefit from doing some user interface (UI) prototyping to explore the requirements.  UI prototyping is an important requirements exploration technique regardless of paradigm, and it is something that you should consider doing during both initial requirements envisioning as well as throughout the lifecycle to explore detailed issues on a just in time (JIT) manner.
3. Holding "all-hands reviews".    One strategy for getting feedback from a wide range of people is to hold an "all hands review" where you invite a large group of people who aren't working on a regular basis with your team to review your work to date.  This should be done occasionally throughout the project to validate that the input that you're getting from your stakeholder represenatives/product owners truly reflects the needs of the stakeholders which they represent.  The 2010 How Agile Are You? Survey found that 42% of "agile teams" reported running such reviews.
4. Increased requirements exploration.  Simple modeling techniques work for simple domains.  Complex domains call for more complex strategies for exploring requirements.  The implication is that you may want to move to usage scenarios or use cases from the simpler format of user stories to capture critical nuances more effectively.  A common misunderstanding about agile is that you have to take a "user story driven approach" to development.  This is an effective strategy in many situations, but it isn't a requirement for being agile.
5. The use of simulation.  You may want to take your prototyping efforts one step further and simulate the solution.  This can be done via concrete, functional prototypes, via simulation software, via play acting, or other strategies.
6. Addition of agile business analysts to the team.  Analysis is so important to agile teams we do it every day.  In situations where the domain is complex, or at least portions of the domain is complex, it can make sense to have someone who specializes in exploring the domain so as to increase the chance that your team gets it right.  This is what an agile business analyst can do.  There are a few caveats.  First, even though the domain is complex you should still keep your agile analysis efforts as light, collaborative, and evolutionary as possible.  Second, this isn't a reason to organize your team as a collection of specialists and thereby increase overall risk to your project.  The agile analyst may be brought on because their specialized skills are required, but the majority of the people on the team should still strive to be generalizing specialists.  This is also true of the agile analyst because their may not be eight hours a day of valuable business analysis work on the team, and you don't want the BA filling in their time with needless busy work.

The important thing is to recognize that the strategies which work well when you're dealing with a simple domain will not work well for a complex domain.  Conversely, techniques oriented towards exploring complex domains will often be overkill for simple domains.  Process and tooling flexiblity is key to your success.