In many Lincoln-Douglas resolutions, Utilitarian reasoning supports one side of the resolution and Categorical Imperative analysis supports the other.
For example: Resolved: When called upon by their government, individuals are morally obligated to risk their lives for their country.
If you were arguing the affirmative side of this debate, you might consider using a utilitarian approach using the argument that some people risking their lives will maximize the benefit for the whole (the country).
If you were arguing the negative, however, you might use the Categorical Imperative saying that treating people as means to ends is inherently unjust.