If I want to rhyme with a word like 'time' would 'overtime' or 'anytime' count as a rhyme with 'time', saying that 'anytime' and 'overtime' have the word 'time' in it. (This goes for any other words)
A syllable consists of two parts: an 'onset' and a 'rime'. It is the final rimes that should match to make a rhyme. Penultimate rimes and syllables may also match; however, the onsets that precede those patterns should not match.
Word breaks (white space) are of minor importance in speech, so 'overtime' works the same as 'over time' for rhyming.
Thus 'great office holder' rhymes perfectly with 'late office holder' and weakly with 'bait off his shoulder', but not with either 'green office holder' or 'grate off his shoulder'.