Hi @AliceR
It sounds like you are looking for something like the "moderated grading" that is available for assignments? (See https://community.canvaslms.com/t5/Instructor-Guide/How-do-I-add-a-moderated-assignment-to-be-graded... ). Is that correct?
There is no equivalent feature available for quizzes, as far as I know. Two teachers can both grade a student's quiz submission, but the second one will overwrite the first's grades on any questions that are manually graded.
You can set the quiz grade to be hidden in the grade book, but that does not necessarily prevent students from seeing feedback.