Is it reasonable to have a factor with only two levels in a carry-over design for an fMRI study? I'm planning a carry-over design for an fMRI study.

To save time, since it seems that I'll need a huge number of trials for my purpose, I'm wondering if it's reasonable to have a matrix 2x3x3, meaning that one dimension has only 2 levels instead of 3 as the others do.
I'm not an expert in neuroimaging, so I had to search a little bit to learn about how carry-over designs apply to fMRI (I found Aguirre, 2007). Thus, feel free to correct me if there is something specific about this problem domain that influences the correct answer to this question.

However, based on general principles of experimental design of repeated measures experiments, you always have to choose


how many factors you want,
how many levels you want for each factor,
what levels you have for each factor, and 
what factors you hold constant.


The particular levels you choose are directly tied to your research question. There are often trade-offs between the cost of resources required to have more experimentally manipulated levels and the benefit of additional questions that can be answered. Thus, I don't think a black and white answer can be given. You need to weigh up the pros and cons. 

And presumably you have already made many experimental design decisions to get to this point. There's nothing magical about 3 levels to a factor. If anything, in experimental psychology two levels seems more common. And you could have four or five or more.

References


Aguirre, G.K. (2007). Continuous carry-over designs for fMRI. Neuroimage, 35, 1480-1494. HTML