If you bring a large suitcase or two, is there enough room in the cabins to store it?

yes
slide it uder the bed or stand it up beside the clothes closet.

Oh yes, there is plenty of room in the cabins to store luggage. Empty your clothes the first day into the closet or dressers drawers. Then slide your empty suitcase under the beds or in the closet.

FYI...not all luggage can fit under the beds

My large Delsey piece fit on Holland America, but not on Princess.

It was up against the wall the entire 10 days

I had a suitcase that wouldn't fit under the bed (just once) and the cabin steward stored it in a room they have for such things. That was on Princess.

I do prefer to keep the suitcase in the cabin (99% of the time they fit under the bed). As a very seasoned cruiser I have learned if I am not going to wear something again I put it directly into the case. By the end of the cruise my packing is minimal - and of course my closet space grows.

Someone gave me this tip ...
Save one of those clear zippered bags that big blankets / comforters come in... bring it along for extra storage under the bed in-cabin,

Never been on a big cruise, but someday.

I love the idea of large plastic bags to keep under the bed! I wish I'd thought of this, as we ran out of space for gifts.