Yes. If the Universe evolves at all scales, then a new method would consist in this:

- When devising an experiment, understanding that whether it works or not isn't linked to it being "true" or not, but whether its success would lead the evolution of the Universe and our human civilization to a dead end or not.

- Allowing for the possibility that different "collectives" of people can interact with reality in a different way besides the scientific method. For instance, that a shaman can heal someone as well as a doctor.

- Let each human choose his/her belief system and way of interacting with reality, in much the same way as different areas in your brain do different things, play different roles.

- Putting humans into a broader perspective: we are the link between the "material" Universe and the "non-material" Universe. What we have the "power" to do is to manifest into "physical" form something that is non-physical. Just look around you and you'll understand. There is no seed that you can plant into the ground which will grow a computer or a chair. These objects are ideas (non-material) which have taken material form through humans. The "realm" of ideas is unlimited. But the ability to create a stable reality out of all of these ideas is limited. We would have self-destroyed us a long time ago if we had "manifested" in physical form ideas like Superman. Therefore, science and the scientific method played the same role as the little wheels you put on the side of kid's bike when he learns to ride a bike: it prevents him/her to fall and hurt him/herself too much. Scientific materialism artificially restricts the way we can "manifest" non-material ideas into physical form. There is no "rule", no "limit", only a limit linked to the ability to construct a stable and durable experience out of those rules. The same applies to a child: as a child matures, he is more and more "free" to interact with the world without artificial limits placed there by his/her parents.