You seem to just be talking about model contrasts, i.e. how you choose to compare different factor levels.
You might want to read a bit about contrasts to understand what they are doing, how they work etc, as they can be a bit confusing to get your head around. Some useful references are:
https://stackoverflow.com/questions/2352617/how-and-why-do-you-use-contrasts-in-r
http://www.ats.ucla.edu/stat/r/library/contrast_coding.htm
However, a very simple way to compare B with C is just to recode your factor levels so that level B is taken as the baseline in R, and then you can use summary() to present the results, which will show you the comparison between the estimated mean values of level B and C.
To recode your factor (here called "your.factor") just use:
your.factor <- relevel(factor(your.factor), "b")
Alternatively, you can use the glht function in the multcomp package in R, although this will take a bit more investigation and learning about how to use it, and you might well be content with using the above solution, given you just need one extra comparison (glht is really useful when you need to specify many different comparisons not given by default, and to correct for multiple comparisons).
Hope that helps.