Synonyms of 'keep off something'
▷ See keep
I managed to stick to the diet and keep off sweet foods.
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If a person or vehicle avoids someone or something, they change the direction they are moving in, so that they do not hit them.
He had ample time to swerve and avoid the woman.
He has repeatedly dodged the question.
If you eschew something, you deliberately avoid doing it or becoming involved in it.
He eschewed publicity and avoided nightclubs.
Thesaurus for keep off something from the Collins English Thesaurus