If there is a latent construct underpinning the current true/false dichotomy then it may be possible. If the dichotomy is mutally exclusive (e.g., gender) then it is not. So let us assume that the latent construct you wish to measure may be scaleable and retain conceptual meaningfulness. For example, the construct vocational interest is useful. An item "Are you interested in X?" requires a dichotomous Yes/No response. If the item were worded, "to what extent are you interesed in X?" then latent factor may be reflected in a categorical scale ranging from low to high, because some people may have no interest, a little interest, a moderate interest, or a passionate interest.

How could you go about doing this? With a binary variable how could you add more options to it?

I think it'd be okay as long as your new category labels make sense. If the original form was T/F, then the new labels could be "Strongly disagree - ... - Strongly agree". It would also simplify the analysis, since factor analysis with binary indicators can give weird results sometimes.

If there is a latent construct underpinning the current true/false dichotomy then it may be possible. If the dichotomy is mutally exclusive (e.g., gender) then it is not. So let us assume that the latent construct you wish to measure may be scaleable and retain conceptual meaningfulness. For example, the construct vocational interest is useful. An item "Are you interested in X?" requires a dichotomous Yes/No response. If the item were worded, "to what extent are you interesed in X?" then latent factor may be reflected in a categorical scale ranging from low to high, because some people may have no interest, a little interest, a moderate interest, or a passionate interest.