Can my students sit Cambridge IGCSE Combined Science 0653 with Cambridge IGCSE Biology 0610, Chemistry 0620, Physics 0625, or Co-ordinated Science 0654?

No, not in the same series of exams. In a single series of exams some combinations of syllabuses are not allowed and you should refer to section 5 ‘What else you need to know’ in the Combined Science 0653 syllabus to find out the exceptions when combining IGCSE Combined Science with other Cambridge International syllabuses.