3 Band Crossover with Linkwitz Riley Filter
A 2nd-order Linkwitz-Riley crossover needs 1st-order allpass phase compensation.

The Lowpass half of the LR crossover is:

$$\dfrac{1}{s^2+2s+1} $$

The Highpass half of the LR crossover is:

$$\dfrac{s^2}{s^2+2s+1} $$

With even-order LR crossovers, in order to sum-to-allpass one of the two sections has to have inverted polarity. Thus:

$$\dfrac{s^2}{s^2 + 2s +1} - \dfrac{1}{s^2 + 2s +1}= \dfrac{(s-1)(s+1)}{(s+1)(s+1)} = \dfrac{(s-1)}{(s+1)}$$