Most brigandines are covered with a cloth foundation, to which the plates are riveted, but they don't have a liner; the bare plates usually rest against whatever arming doublet or haubergeon was worn underneath. However, the brigandine from the Castello Sforzesco in Milan has an integrated mail liner.
http://wratislavia.archeo.uni.wroc.pl/18-tom/9.pdf

I was wondering whether there are any other extant brigandines with mail liners.

my first thought is, would the way the mail is mounted to the bringadine provide too rigid a contact surface/ a slightly taut mail fabric, and maybe cancel out the benefits that maille might normally have?

if not, it seems a brilliant thing to add to augment the armour

I have seen other pictures of this armor, and when I look at it, it seems to me that the mail is acting as a substitute for further plates, and that the plates that are present are connected to both the mail by the plate edges and to the fabric with rivets as the plates usually are. It may be that this could be made from a torn or otherwise undesirable shirt fragment repurposed as new armor, it may be for fashion, as it can adjust or hug very closely to the body, or it may be a lighter armor designed to bridge a gap between a straight mail shirt and a regular brigandine.

The plates may well be layered atop the mail, and may be attached to just the mail or to the fabric through the mail; I cannot say. I am also unsure of the presence or absence of further plates than those readily visible, or whether or not more plates were initially present. I did find this, however:

https://www.pinterest.com/pin/7881368072058503/

I would agree that it looks like a brigandine where many of the back plates are instead replaced with mail. As far as I can tell, it doesn't feature mail on the front part - that's just made of plates.

It seems in some ways a precursor to the idea of a mailed jack, which I seem to recall turning up later (see also jacks of plate and so on)