Adding a phone number that people KNOW about can make it LESS secure. A workaround is to get a phone number that is only used for identity verification and not given out to anyone.
It's not fun to have 2 phones always with you. But maybe the 2-SIM devices will become more mainstream soon, which can solve this problem.
It's possible if you use something like Google Voice for most of your regular calls, but you still need to make sure that the telco can't tie your name to your number…