No, because a coalition agreement must be exclusive. If small party X pledges to being in a coalition with, say, Labour, there is no way that Labour would allow them to team up with anyone else.
How would Labour enforce this? Because being in a coalition is mutually beneficial. In exchange for party X giving Labour their votes, Labour promise to implement some of party X's policies (and maybe refrain from implementing some of Labour's policies that party X don't like).
If party X break this agreement, Labour would lose their votes - but party X would lose all their influence, along with any chance of their policies being turned into law.
Whether or not party X go so far as to team up with another party, Labour would remain in government until either they lost a confidence vote, or a general election was called (either by a 2/3 majority of the Commons, or 5 years after the last election).
Note that the current government stays in place until either the PM feels that she has enough votes to stay in government (whether as a coalition, or as a minority government with some kind informal agreement with other parties), or it become obvious that another party or coalition has the votes.
For example, in 2010 Gordon Brown stayed as PM for 5 days after the election, until it became clear that the Conservatives and LibDems had the numbers for a coalition. The LibDems did also have talks with Labour about forming a coalition, but the numbers didn't add up.