"take different stance" is correct and usable in written English.
You can use it when talking about taking a position on a particular issue or topic, or when talking about an individual taking a point of view which differs from the opinions of others. For example, "When facing social issues, many politicians take different stances depending on how their party's platform is framed."
Business schools take different stances on the issue.
The SNP also questioned whether Scottish Labour and Labour at Westminster could take different stances on the policy, with the possibility of them abstaining at Thursday's vote.
Philosophers take different stances on what legitimate justifiers may be, so that it is difficult to come up with an account of justifiers that is neutral between competing theories of epistemic justification.
Remuneration modalities appear in all of the interviews as structuring conditions for GP activities and decisions, even if the GPs take different stances toward them as we have shown above.
The court took different stances in cases involving Muslim and Buddhist death-row inmates.
Insurers are also taking different stances on how they treat the warning "against all but essential travel" to coastal areas within 150km of the Somali border due to threat of kidnapping, and to areas within 60km inland from that coastal strip and the Garissa District because of continuing instability in these areas.
Banks, governments and regulators seem to all be taking different stances on action toward ICO's and regulation of the Blockchain system in general.
So far, supermarket chains have taken different stances toward selling organics.
Although religious groups take different ethical and moral stances on issues such as sexuality, this should not (and, I believe, usually does not) prevent them from offering aid to all in need.
You don't have to take a different stance about a woman's right to choose.
Now, if we fail to deliver them and we have to take a different stance, then that's a new situation.
