I traveled openly on two passports (US and Irish) in Southern Africa in 1998. My traveling partner had three (US, UK and Australia). Border officials were generally insistent that we use only one of our passports for the whole trip to ensure an unbroken series of entry and exit stamps.

On that trip I entered South Africa on my US passport and then learned that many of the counties I would be visiting had high visa fees for US passports but no fees for Irish ones. From then on, at each border, I tried to switch over from my US to the Irish one. On departure from each country I presented the Irish passport and invariably the official would refuse to stamp that passport because it lacked a valid entry stamp into his country. I then presented the US one and received the correct stamp. In the next county on the other side of the border their official wanted to see the stamp from the country I just left, etc, etc. I eventually found a very sleepy Zimbabwean immigration officer on the Botswana border who didn’t look for the old stamp in my Irish passport, allowing me to use it for the rest of my trip.

Only one border official gave us any grief about having two passports. I called his supervisor who agreed with me. The concept is fairly easy to explain to border officials but has to be done gently: Legally, citizenship is a matter for the passport issuing country. For example, if the US and Ireland both issue a passport to an individual that is a matter for the US and Ireland. A country such as South Africa has no legal jurisdiction over the issuance of these passports because it happens overseas to a foreigner. As always though the most powerful tool for crossing a third world border is a big smile and a friendly approach.
Good luck. Have a great trip.
Brian.