  In this paper, we extend the rectangular side of the shuffle conjecture by
stating a rectangular analogue of the square paths conjecture. In addition, we
describe a set of combinatorial objects and one statistic that are a first step
towards a rectangular extension of (the rise version of) the Delta conjecture,
and of (the rise version of) the Delta square conjecture, corresponding to the
case $q=1$ of an expected general statement. We also prove our new rectangular
paths conjecture in the special case when the sides of the rectangle are
coprime.
