Changing the domain set for first-party cookies?

[jereze]

According to the documentation:
By default, the cookies are set on the domain specified by document.location.host (ie, the "current website") on the / path.

Is there an option to attach first-party cookies on .domain.tld (starting with a dot) instead of, for example, www.domain.tld?

It could allow to get the same cookies for all sub-domains of the same level.
From the RFC 2109:

A Set-Cookie from request-host x.foo.com for Domain=.foo.com would be accepted.
A Set-Cookie from request-host y.x.foo.com for Domain=.foo.com would be rejected, because H is y.x and contains a dot.