Multi-Class Characters (CPrH)

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It's possible for demihumans to be multi-class combinations including the priest character classes above.
On the chart of the Player's Handbook, page 44, showing the possible multi-class combinations, substitute the word "priest" wherever you see "cleric." Those are the possible combinations.
The only limit the character possesses on which type of priest he may be is the racial limitation posed for each priest-class above. If a priest-class says that elves can't belong to it, then obviously an elf can't be a multi-class fighter/priest of that type of priesthood.
Multi-class priest characters follow all the rules for multi-class characters, from pages 44 and 45 of the Player's Handbook.