Liverpool has Aer Lingus to Dublin. Not strictly Oneworld but will get you Avios and TPs.

MAN is well served by Oneworld. The airport is not my favourite (it’s better now than it was in 2018/19 but still not good). Depending on precisely where you live, you may find the train to London and then the Liz Line to LHR is preferable to flying from MAN (I face a similar dilemma in Leeds). In terms of flights though you have Finnair if you’re going east alongside CX and QR, Aer Lingus (previous proviso applies) to New York, Orlando and Barbados and a smattering of Iberia and Royal Air Maroc flights alongside BA. It’s not bad as far as outstations go from that point of view!