What are some possible advantages of having only two powerful political parties?

I can think of one advantage: if this party wins, it will have a majority in the parliament and senate, so it will be have more power and would not have to negotiate every voting with the other party in the coalition.

In a multiple party when coalitions , the smaller party in the coalition usually gets proportionately much more power because it can "blackmail" the bigger partner; this often stalls the voting process. 

The president's only official legislative duty is to sign or veto bills.