Can I have 4 copies of each Alph Lithograph card in my deck?
No, you may not. Each variant of Alph Lithograph does something different, but they all have the same card name. Just like you can have no more than 4 Pikachu in any combination, you can only have a maximum of 4 Alph Lithograph cards in your deck. When entering onto a decklist, make sure to list them on separate lines and include the set and card number on each line for clarity.
Source: PUI Rules Team (2011-09-15)

Relevant cards

Note: All applicable cards may not be listed below.
HGSS1_ONE
HGSS2_TWO
HGSS3_THREE
HGSS4_FOUR