  We compute $M$-point conformal blocks with scalar external and exchange
operators in the so-called comb configuration for any $M$ in any dimension $d$.
Our computation involves repeated use of the operator product expansion to
increase the number of external fields. We check our results in several limits
and compare with the expressions available in the literature when $M=5$ for any
$d$, and also when $M$ is arbitrary while $d=1$.
