  Owing to comparably strong spin-orbit coupling and Hubbard interaction,
iridium based 227 pyrochlore oxides harbor a rich confluence of competing
magnetic orders and emergent multipolar Weyl quasiparticles. Here we show that
this family of materials is predominantly susceptible toward the nucleation of
electronic noncoplanar all-in all-out (AIAO) and three-in one-out (3I1O)
orders, respectively transforming under the singlet $A_{2u}$ and triplet
$T_{1u}$ representations, supporting octupolar and dipolar Weyl fermions, and
favored by strong on-site Hubbard and nearest-neighbor ferromagnetic
interaction. Furthermore, a collinear magnetic order generically appears as an
intermediate phase between them. This order transforms under the triplet
$T_{2u}$ representation and also hosts octupolar Weyl fermions. With the AIAO
and 3I1O phases possibly being realized in (Nd$_{1-x}$Pr$_{x}$)$_2$Ir$_2$O$_7$
when $x=0$ and 1, respectively, the intervening $T_{2u}$ order can in principle
be found at an intermediate doping ($0<x<1$) or in pressured (hydrostatic)
Nd$_2$Ir$_2$O$_7$.
