Creating GA4 cookie with third-level domain

Hi, is it possible to set a first party a cookie with a third level domain like www.example.com even when my server is hosted on measure.example.com? Has anyone done it before? Are there any limitations regarding the stape hosting?
Thank you
Tomas

the cookies are most commonly set for the top level domain so for .example.com therefore they are shared across all subdomains of this tld. Bottom line is yes, it’s allright and it will work.

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Thank you, Dan. By the way is it possible to set the first party cookie even when the server is hosted on different top level domain? let say hosted on measure.example.work and the cookie would be for www.example.com?

no, not possible, that would be a 3rd party cookie.