You might be able to use the Arcam to power your main speakers and also use the pre-out from the Arcam into the Adcom amp and let the Adcom power the in-walls. Playing more than 2 pair of speakers from one amp is typically not advisable due to the lowering of the impedance as you add speaker pairs. Of course, if you have some type of impedance matching speaker control box in the system, this does not apply.
Most amps (including integrated amps and receivers) are typically spec'd to power (up to) two pair of 8 ohm speakers. Two pair of 8 ohm speakers equals 4 ohms. Adding yet another pair to the same amplifier outputs would lower the impedance ever further and that is typically not advisable. Splitting your multiple pairs of speakers between 2 or more amps, such as using both the Arcam and the Adcom, would overcome this potential issue.
Most amps (including integrated amps and receivers) are typically spec'd to power (up to) two pair of 8 ohm speakers. Two pair of 8 ohm speakers equals 4 ohms. Adding yet another pair to the same amplifier outputs would lower the impedance ever further and that is typically not advisable. Splitting your multiple pairs of speakers between 2 or more amps, such as using both the Arcam and the Adcom, would overcome this potential issue.