N2 — outside your level filter

ないものだろうか

ないものだろうかnai mono darou kaN2neutral

heal + not + isn't there some way — a hopeful wish something could still happen

naoranai mono darou ka

isn't there some way — a hopeful wish something could still happen

meaning: isn't there some way to heal

何なんとかできないものだろうか。

nantoka dekinai mono darou ka.

Isn't there something we could do about this? neutral

迷子まいごになったあの子こ、早はやく治なおらないものだろうか。

maigo ni natta ano ko, hayaku naoranai mono darou ka.

That lost child — isn't there some way to heal soon? casual

All examples3

isn't there some way — hoping a stuck situation could still turn around

何なんとかできないものだろうか。
nantoka dekinai mono darou ka.
Isn't there something we could do about this? neutral
迷子まいごになったあの子こ、早はやく見みつからないものだろうか。
maigo ni natta ano ko, hayaku mitsukaranai mono darou ka.
That lost child — isn't there some way to be found soon? casual
何なんとか納期のうきを延のばしてもらえないものだろうか。
nantoka nouki o nobashite moraenai mono darou ka.
Might there be some way we could get the deadline pushed back? neutral

ないものかnaimonokaalternant
治なおらないものか
drops だろう and keeps just か. reads a little more resigned and less like an open question.