Hi Louise,
ditto Brainless & Missie - I'd get further checks done sooner rather than later. Discuss with vet possibilities of giardia and SIBO too - both relatively easily treated with meds

TBH I'm not a believer in the allergy tests done by York etc - they are not always accurate and unless covered by insurance probably not worth paying out the cost of at this point. I'd have the faecal sample and bloods done to rule out serious ailments and if intolerance was then the most likely cause I'd go down the exclusion trial route

As Missie suggested before, give one ingredient at a time for at least a week then add another and when your friend gets to (say) 3, stick with those alone for a minimum of 8 weeks providing there are no obvious diverse effects. Then gradually introduce another ingredient - any problems arising this way are easily recognised, identified and can be discarded from the dog's diet. It is a lengthy process but a reliable one
EDITED to add I would probably go down the route of a home prepared and/or raw diet - even ingredients known to cause problems can often be fed raw when not possible to cope with after processing.