  In 1926, Levi showed that, for every pseudoline arrangement $\mathcal{A}$ and
two points in the plane, $\mathcal{A}$ can be extended by a pseudoline which
contains the two prescribed points. Later extendability was studied for
arrangements of pseudohyperplanes in higher dimensions. While the extendability
of an arrangement of proper hyperplanes in $\mathbb{R}^d$ with a hyperplane
containing $d$ prescribed points is trivial, Richter-Gebert found an
arrangement of pseudoplanes in $\mathbb{R}^3$ which cannot be extended with a
pseudoplane containing two particular prescribed points. In this article, we
investigate the extendability of signotopes, which are a combinatorial
structure encoding a rich subclass of pseudohyperplane arrangements. Our main
result is that signotopes of odd rank are extendable in the sense that for two
prescribed crossing points we can add an element containing them. Moreover, we
conjecture that in all even ranks $r \geq 4$ there exist signotopes which are
not extendable for two prescribed points. Our conjecture is supported by
examples in ranks 4, 6, 8, 10, and 12 that were found with a SAT based
approach.
