A bit OT, but if you REALLY want to ALWAYS be reachable, no such thing in some spots, but you can greatly increase the odds with the following.
Set up a dedicated new gmail account, then sign that up for gVoice or whatever they're calling it these days, when I started it was called "Grand Central".
Give them a geographical location that is most likely to result in them assigning you an area code/exchange prefix number you like.
Set that gVoice number up to automatically forward to all your numbers, but don't give it out to anyone (yet) except for testing purposes. When someone calls in, all the phones on that forwarding list will ring at the same time - pick up one of them, the rest will stop.
Texts sent to this number will get forwarded to the cell numbers you specify.
Google also gives you a most excellent voicemail service, automatically transcribes and forwards to SMS and/or attaches sound files to email, whatever you want.
Test this stuff out for a while with your Verizon service (I assume primary voice cellphone as well as data?)
Meantime, sign up for cheap prepaid service on throwaway phones that use AT&T, T-Mobile and Sprint.
Truphone uses ATT and T-Mobile, if you don't use it for voice much outbound, it is basically free after your initial sign-up, and they don't charge at all for accepting inbound calls. Also excellent for when you go overseas.
Google Fi is a carrier that consolidates service between those last two an integrates with the gVoice number above, about $20 / mo, if that's not too much, highly recommended.
Otherwise, FreedomPop has a free service on Sprint.
For details and recommendations on the wide world of low-cost no-contract phone services, I highly recommend a website called howardforums.
As you sign up for these "extra coverage" services, add the new numbers to your gVoice forwarding list. You don't have to have them all on at the same time, but when you notice you don't have a signal with Verizon try the AT&T one , and then the others until you get a strong signal good for that area, and then turn the others off.
Once you're comfortable with this scenario, go "into production".
Choose the inbound number the greatest number of contacts important to you know as your "main number", and "port it over" to Google Voice, tell them you want it to be your main number and the temp/testing one they originally gave you will go away.
If you want you can have multiple inbound numbers, but that isn't free, I think one time $25 charge.
One big advantage of the Google 5 services is that all of your outbound calls from that phone will show
that main number , the one all of your contacts are familiar with.
You can make calls using that number from a computer , voice over IP with the Google Voice service comma also very low rates for calling overseas.
When you're making calls from your temporary / burner phones because you're out of range , just let people know to ignore those numbers and if they want to call you back use the main numbers that they already know.
However, most services are easy to setup to use external voicemail comma so if you do that with those prepaid burner phones, when you have them turned off at least the messages will come into your unified voicemail box.
Set up a dedicated new gmail account, then sign that up for gVoice or whatever they're calling it these days, when I started it was called "Grand Central".
Give them a geographical location that is most likely to result in them assigning you an area code/exchange prefix number you like.
Set that gVoice number up to automatically forward to all your numbers, but don't give it out to anyone (yet) except for testing purposes. When someone calls in, all the phones on that forwarding list will ring at the same time - pick up one of them, the rest will stop.
Texts sent to this number will get forwarded to the cell numbers you specify.
Google also gives you a most excellent voicemail service, automatically transcribes and forwards to SMS and/or attaches sound files to email, whatever you want.
Test this stuff out for a while with your Verizon service (I assume primary voice cellphone as well as data?)
Meantime, sign up for cheap prepaid service on throwaway phones that use AT&T, T-Mobile and Sprint.
Truphone uses ATT and T-Mobile, if you don't use it for voice much outbound, it is basically free after your initial sign-up, and they don't charge at all for accepting inbound calls. Also excellent for when you go overseas.
Google Fi is a carrier that consolidates service between those last two an integrates with the gVoice number above, about $20 / mo, if that's not too much, highly recommended.
Otherwise, FreedomPop has a free service on Sprint.
For details and recommendations on the wide world of low-cost no-contract phone services, I highly recommend a website called howardforums.
As you sign up for these "extra coverage" services, add the new numbers to your gVoice forwarding list. You don't have to have them all on at the same time, but when you notice you don't have a signal with Verizon try the AT&T one , and then the others until you get a strong signal good for that area, and then turn the others off.
Once you're comfortable with this scenario, go "into production".
Choose the inbound number the greatest number of contacts important to you know as your "main number", and "port it over" to Google Voice, tell them you want it to be your main number and the temp/testing one they originally gave you will go away.
If you want you can have multiple inbound numbers, but that isn't free, I think one time $25 charge.
One big advantage of the Google 5 services is that all of your outbound calls from that phone will show
that main number , the one all of your contacts are familiar with.
You can make calls using that number from a computer , voice over IP with the Google Voice service comma also very low rates for calling overseas.
When you're making calls from your temporary / burner phones because you're out of range , just let people know to ignore those numbers and if they want to call you back use the main numbers that they already know.
However, most services are easy to setup to use external voicemail comma so if you do that with those prepaid burner phones, when you have them turned off at least the messages will come into your unified voicemail box.