In message , at 13:11:43 on Thu, 8 Oct
2020, Andy Burns remarked:
Roland Perry wrote:

I'd like to add a room thermostat in the living room [running
additional wiring isn't an issue] but need to know if it can simply
be put in series with the timer-control.

I'd use a programmable thermostat in the living room then either remove
the existing timer, or set it "on" 24x7.

the new stat can then have different temperatures at different times of
day, or days of week. Use a wifi prog-stat if you want to control it
from a browser or phone.

Sounds a bit complicated.
--
Roland Perry