That has happen. UKIP forced the Conservative Party in the UK to offer a referendum because their members were voting for UKIP (UKIPs voter share in 2015 hit about approximately 13% of the total vote). Whatever you may think of UKIP

https://www.bbc.co.uk/news/election/2015/results

However there is several negatives to this:

1) That political party won't get any credit for it. 2) The policy will be implemented hardheartedly. 3) It may destroy your party if one or more of the major issues that the alternative party is implemented. As voters won't see any more need to vote as they have got what they wanted. 4) Thee political momentum will be lost for other reform / change. 5) The existing party duopoly will still exist.

To expand on the final point. I dislike all political parties (I am somewhat of a anarchist) and I don't believe in political solutions. However the Labour party in the UK immolating itself will hopefully end up with its destruction. Which will make space in the UK political landscape for new ideas, new people. Some speculate that it may also lead to the destruction of the Conservative party. Peter Hitchens described both Labour and Conservative parties as two corpses that are propping the other up and if one collapses the other may as well. However I personally think that is a fantasy.