Is the man you met good-looking and have a stable job?
Is it vegan and have high protein?
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You can only do this if the root verb (the first do, is, have, or modal) is the same for both. If it isn't, you have to "start over".
Did he walk to the park and find the playground?
Is he walking to the park and did he find the playground?
Is he walking to the park and looking for his cousin?
Also note that at least in AmE, possessive have always requires do in questions.
Is it vegan and does it have high protein?
Has/have/had as part of a perfect verb construction can take the place of do or is and that does not take a do/does/did.