You probably want to program the other tower's control channel into your scanner if you haven't already done so. If the tower goes completely offline, then the PSR-600 will check the other control channel and lock onto it. If the tower does not go completely offline and still has a control channel, then you likely want to use the Stationary (Stat) Multi-Site mode and have Check All CC mode set to on (all these options found under the TSYS menu).
Sadly, the PSR-600 and all it's clones do not have the option of selecting individual sites to check or lockout, so it depends heavily on things like the Multi-Site feature. What the settings will do is force the PSR-600 to check all control channels it has programmed when in scan mode and therefore pick up traffic on other towers that it can hear. This will allow it to pick up on traffic off of other towers instead of just being forced to stay on a single tower.
The alternative solution is to duplicate your TSYS and any associated talkgroup you have programmed into multiple TSYS, then manually adjusting the scanlist or the TSYS lockout in order to specifically target certain towers.