Cell coverage
 

How do I switch my cell coverage to make calls in Mexico without high fees

get a Mexico sim ..... if you want someone in Mexico ( like your hotel) to call you back , they may not be allowed to call a USA number.

if you are calling the USA you can use Skype , and some of the USA carriers include Mexico and Canada in their plans.

Who do you have now ?

Making most of my calls via internet when abroad. Ever heard about https://www.skyroam.com/ ? Been using it several times already and it works quite good anywhere in the world. For true cell coverage the best way is indeed getting a domestic (in this case Mexican) sim card..

what carrier do you use? on TMobile, Mexico (and Canada) to US calling is included in many of their plans.