  We prove that monoids $\mathrm{Mon}\langle a,b,c,d : a^nb=0, ac=1, db=1,
dc=1, dab=1, da^2b=1, \ldots, da^{n-1}b=1\rangle$ are congruence-free for all
$n\geq 1$. This provides a new countable family of finitely presented
congruence-free monoids, bringing one step closer to understanding the
Boone--Higman Conjecture. We also provide examples which show that finitely
presented congruence-free monoids may have quadratic Dehn function.
