"Packed to the rafters" is an idiom that means a place or space is full to capacity. There are various synonyms to this phrase that can be used depending on the situation. For instance, "jam-packed" emphasizes a very dense and crowded situation. "Stuffed" signifies an overfilled or crowded space with no room to move. "Teeming" implies a lively and bustling place that is brimming with activity. "Chock-full" suggests a space that is filled to the brim with a specific item or content. "Brimming" implies that a place is close to overflowing with things or people. Other alternatives may include "crowded," "overfull," "crammed," or "thronged." In summary, these synonyms can help add variety and intensity to one's speech or writing when describing a situation that is full to capacity.