The best examples that come to mind are when ordering food. As examples:
• You speak English and Spanish and are ordering a burrito
• You speak Thai and English and are ordering Tom Yum
I imagine it could depend on numerous things:
• You primary language or ethnicity
• What sort of restaurant
• Who you’re dining with
• Who you’re ordering from
• and probably a lot more…
I’ll pronounce Spanish words in an American accent, but using Spanish pronunciation. For example, if I say “I would love a quesadilla, but I don’t have any queso or tortillas.” I’ll pronounce the “que” as “kay” instead of “kway” and the “illa” as “eeya” instead of “ila”, but in an American accent. The exception being if I’m pronouncing a place name, then I’ll pronounce it with English pronunciation. Like “Los Angeles”, I pronounce as “loss anjiless”.