Ezekiel 42:6
The three part structure had no columns, unlike the courts, which is why the upper chambers were offset from the ground upward, more so than the lower and middle chambers.
Ezekiel 41:6
The side chambers consisted of three stories, each above the other, with 30 chambers in each story. The side chambers extended out from the wall that faced the inside of the chambers where the chambers were fastened together, but the chamber walls were not fastened directly into the Temple walls themselves.
1 Kings 6:8
A passageway to the side chamber was constructed on the south side of the Temple by which people could ascend winding stairs to the middle story, then from there to the third story.