The inventory on the EnTama (and UraTama) works differently than on the V3.
On the V3 you might see:
1 Royal Costume
2 Mirror
3 Gramophone
4 Ticket (Hawaii)
5 Ticket (Switzerland)
6 Music Disc
7 Ticket (China)
8 Ticket (Chile)
9 Shirt
10 Sun Glasses
11 Chest
12 Plant
13 Plant
14 Fishing Pole
15 Plant
16 Shovel
17 Shovel
18 Pencil
19 Pencil
20 Music (Walkman)
21 Plant
Each entry in the list represents one item. The number indicates its location in the list. If you have two (or more) of the same items they will occupy two (or more) spots on the list. Notice there are multiple entries for Plant, Pencil, and Shovel. Once all the spots on the list get filled, you can't get any more items.
On an EnTama (or UraTama) you might have a list like this:
- Bananas
- Ice Cream
2 Rice Crackers
3 Milk
3 Tea
3 Chocolate
3 Parfait
3 French Fries
3 Candies
Each entry on the list represents a type of item you have. The number represents how many of them you have. (If there's no number, it's a built-in item - you have an infinite supply of it.) If you have 2 Rice Crackers and get another one, the other one won't show up as a new entry on the list, instead the existing entry will change to 3 Rice Crackers.
There is a maximum number of each item you can have. The maximum depends on each item. For some it's 1, for others it's 3.
I think you can have every item available. The number of spots on the list is equal to the number of different items available for the EnTama (or UraTama).