I've used more than one passport many times at many borders.
Rule number 1: ALWAYS use the same passport to leave a country as the one used to enter.
By air, no problem to change passports; by land you may run into a situation where the immigration agent at your entry point will expect to see an exit stamp from the previous country in the passport you use to enter the country. I've had this only once and on that occasion was able to return to the previous immigration ("emigration") office and obtain a stamp. However this may not work everywhere, so in general seek to use the same passport all the time.
However... some countries will not let you enter if you have a stamp from the "wrong" country. For example if you have an stamp from Israel some countries will not let you enter (e.g., Lebanon, Syria, Yemen, Iran, Libya, Kuwait and Sudan (not sure whether this is up to date)). I've had this only a few times, long ago, and the country involved used to stamp a separate piece of paper which you kept with your passport. I suggest that you check every border you plan to cross for restrictions.
Some countries impose a "reciprocity fee" (if one of your passport countries imposes a fee on its citizens to enter the country, they charge citizens of that country a fee for entry). For example, Colombia now charges a reciprocity fee for Canadian passport holders. When I used to enter Chile I used to use the passport to which this fee did not apply. See above for the possible inconvenience involved.
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