I dont see why not.
The guts in the one you have are just like a FRIEDLAND ding dong, they work off 4 x 1.5 volt bateries so as low as 6 volt.
if you hold the bell button in it just goes DING then silent, so callers let go off the button and it goes DONG so its rarely powered up for long anyway, so I cant see 10 volt harming it.
In addition there will be volt drop in the cable to the second bell, what distance is it to the second location
http://www.friedland.co.uk/en-GB/Chimes/Fixedchimes/Pages/D117.aspx
The guts in the one you have are just like a FRIEDLAND ding dong, they work off 4 x 1.5 volt bateries so as low as 6 volt.
if you hold the bell button in it just goes DING then silent, so callers let go off the button and it goes DONG so its rarely powered up for long anyway, so I cant see 10 volt harming it.
In addition there will be volt drop in the cable to the second bell, what distance is it to the second location
http://www.friedland.co.uk/en-GB/Chimes/Fixedchimes/Pages/D117.aspx