Sometimes our business or personal travel takes us to places which are technically at war with each other or have no diplomatic relations e.g. Iran and Israel (see below). This means if you visit one and have visa stamps in your passport, you may not be allowed to visit the other. Or face some very awkwardly questioning.
1. Ask the agent to not stamp your passport
Cuba and Israeli immigration agents will hand you a separate piece of paper with the visa stamp which sits in your passport.
2. Find your Dual Nationality
Some of us (not me) can have a second passport from a different country. Eg Australia and UK. You can then legitimately enter one country on one passport and the other countr(ies) on the second.
3. Get a second passport
Many nations will issue you with a second passport if you explain where you are travelling. eg the Middle East. You can then use one of these passports for all Arab and Muslim countries and the other one for Israel, Europe and the US. Often, the second passport is valid for fewer years than your primary one. NB It is illegal to enter some countries with two passports so be aware of this and plan accordingly. People and possessions can be searched. Don’t keep both passports together and don’t display two passports at the border crossings! Remember which passport you are using where and don’t try to enter a country with one passport and try to leave with another!!
Some people ” lose ” their passports mid trip. I don’t recommend this option because your passport is officially government property and your actions may be illegal which could cause worse issues later.