Is it possible for  $R^2$ of a regression on two variables be higher than the sum of $R^2$ for two regressions on the individual variables? In OLS, is it possible for the $R^2$ of a regression on two variables be higher than the sum of $R^2$ for two regressions on the individual variables.
$R^2(Y \sim A  + B) > R^2(Y \sim A) + R^2(Y \sim B) $ 
Edit: Ugh, this is trivial; that's what I get for trying to problems issues that I thought of while at the gym.  Sorry for wasting time again.  The answer is clearly yes.
$ Y \sim N(0,1)$
$ A \sim N(0,1)$ 
$ B  = Y - A $
$R^2(Y \sim A + B) = 1$, clearly.  But $R^2(Y \sim A)$ should be 0 in the limit and $R^2 (Y \sim B)$ should be 0.5 in the limit.  
 A: Here's a little bit of R that sets a random seed that will result in a dataset that shows it in action.
set.seed(103)

d <- data.frame(y=rnorm(20, 0, 1),
                a=rnorm(20, 0, 1),
                b=rnorm(20, 0, 1))

m1 <- lm(y~a, data=d)
m2 <- lm(y~b, data=d)
m3 <- lm(y~a+b, data=d)

r2.a <- summary(m1)[["r.squared"]]
r2.b <- summary(m2)[["r.squared"]]
r2.sum <- summary(m3)[["r.squared"]]

r2.sum > r2.a + r2.b

Not only is it possible (as you've already shown analytically) it's not hard to do. Given 3 normally distributed variables, it seems to happen about 40% of the time.
A: It isn't possible.  Moreover, if A and B are correlated at all (if their r is nonzero), the rsq of the regression on both will be less than the sum of their individual regressions' rsq's.
Note that even if A and B are completely uncorrelated, adjusted rsq's (which penalize for a low case-to-predictor ratio) may be slightly different between the two solutions.
Maybe you'd like to share more about the empirical evidence that's got you crossed up.
