I currently run a setup where phones are on 3 different VLANs and it works perfectly well with all these phones connected to a single Asterisk box on a 4th VLAN.
You just need to correctly set the “Local Networks” field and setup routing (generally this is done outside your FreePBX box).
When you say you manage a network with 10 VLANs I tend to think you are a network expert and would have tested routing before seeking for help here. But then if you were a network expert you would have provided more information on your initial post, provide meaningful log data, show that routing is working despite the “cannot ping” symptom you described, etc. So now I am thinking you are not a network expert and may actually be way out of your league with that 10 VLAN network.
Please, if you want help show to us that routing is working as it should. And remember that the routing must work both ways to and from every VLAN involved.
If you need more help with routing issues please give more detail of your network topology, specially inform how your gateways are setup and what is the routing device routing to and from each VLAN.
Good luck!