On GRE radios, the radio will search each site looking for a quality, decodable signal. When it finds one, it will stay with that site/control channel as long as the quality is above a programmable threshhold value. When it drops, the radio will start searching again for a good site.
To get the best results and have total control while "stationary" (i.e. at home, etc.), the best option might be to treat each site as a separate system. That is - duplicate the system and enable only one site in each scanlist. This way, you can enable and disable the site(s) you want to try to receive. This will force the radio to check the control channel for as many sites as you want even if the closest site is coming in at 100% quality.
This can be further improved by reducing the frequencies in each site's programming to either just the primary and alternate control channel frequencies (where applicable) or even just the primary control channel (assuming it doesn't change much or all all). This is especially helpful for systems that display digital simulcast problems where the control channel is likely to fade.
On the other hand, in mobile operations, I'd program all sites into a single system for just those sites along my route (just the CC frequencies) and let the radio pick the right one as I drive.
...and I nearly never touch the default threshhold settings.
Even though the GREs scan fairly fast, the less the radio has to sift through, the faster you'll lock onto something.