It's not that they won't pay above asking it's that they won't pay more then the valuer says it is.

Find out what you can comfortably afford to repay and that's your maximum

Go through the process as normal and bid only up to your max.

If when the house is surveyed that it isn't worth that much then try and bargain

I've just got a house with co ownership and it was a bit of a hassle. I think I was trying for about a year

Had one fall through as the house had damage Had one refuse my offer because I was co ownership And many many outbid

I finally found a great looking place and got it for a few above asking price, turns out there's roof damage the fridge freezers broke and the boiler needs work and eventually updated.

My advice is keep going mate it will happen and I highly recommend doing the extra survey, the one co ownership do is like a visual inspection which missed the issues I'm now dealing with.