I don't think the party should move more centrally or split to have a central side - let the centrists either stay, or if they go too far to the right, join the Lib Dems instead.
I believe this country desperately needs to shift the Overton window back to the left just to reach the centre.
After 9 years of austerity, and many more years before that of Conservative destruction of public services, and no way near enough done by the centrist Labour party in the middle to compensate, we urgently need social democracy to bring things back to decency.
If you think about anything that is good in society, that makes life better, it'll be shared between the people: state education, public libraries, public swimming pools, national utilities, public museums, free parks and open spaces, public toilets, once upon a time decently subsidised public transport, social housing, the NHS. All of these things are there to make society a better place to live in. And all of these things have been under threat, or have been privatised or closed by the Conservatives. We've lost hundreds of libraries, of youth centres, of Surestart centres, of swimming pools, of public toilets - and we've lost access to flexible, subsidised further and higher education.
It isn't radically left wing or communist to want to reinstate some of those things. Because yes, we can all live independently and not share resources, but if we do share them better then the richest people also do benefit - from living in a happy, healthy and cooperative society where there aren't people living on the streets, and where ordinary people have enough money to be able to spend and keep the small businesses afloat around them.
The Labour Party was born to help everyone in society, and to protect the poorest and most vulnerable. The fact that so, so many people are struggling right now shows that society has been atomised too much by the right, and so we on the left should not be talked into moving to centrist 'not quite as bad as the Conservatives' positions. There are very clear moral values going on here, and if it didn't work this time, then another 5 years and Brexit happening is sure to bring more people to vote Labour next time.