It is unlikely such an offer would be accepted.
Nothing is certain, but here are two strategies.
Appoint an Architect, an Engineer and a Solicitor.
#1
A straight garage conversion lying wholly within your boundary.
You will probably want to renew the roof and include new rooflights.
Assuming this does not impose increased loads on the hopefully well-built existing party wall, it should not require trespass or invite approbium from your neighbour.
Get the building professionals to inspect the property and the legal eagle to review the Land Conveyancing Law Reform Act Chapter Three.
Devise a design with the architect which satisfies your requirements and which avoid the party wall.
Devise a structural solution with the engineer that avoids increasing the load on the party wall.
Inform the neighbour of your intention to commence work explain the programme timetable and seek to agree preferred times for commencement an cessation.
If the neighbour is acting up inform him of the rights conferred by said Act.
#2
A conversion with 1st floor extension.
This will involve raising the party wall and may involve revisions to the flashing / sealing of your neighbour's roof.
Get the building professionals to inspect the property and the legal eagle to review the Land Conveyancing Law Reform Act Chapter Three.
Devise designs with the architect which satisfy your requirements and which utilise / avoid the party wall.
Devise structural solutions with the engineer that (i) involves / (ii) avoids using the party wall to support a superstructure.
Draw up a contract to discuss with the neighbour and confirm you would prefer this work to be done with their consent.
Offer to sweeten the pill by allowing them to take bearing off the wall at a future date if required.
If they don't want to deal go for option 2 which stays wholly within your boundary and write to the neighbour confirming the position.
Seek permission if required, including documentary evuidence of discussions with the neighbours if necessary.
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Removal of the wall may not be necessary in either case.
Remember, its good to talk to people living locally.
Ask about your neighbours before buying.
Hope this helps.
ONQ.
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All advice on AAM is remote from the situation and cannot be relied upon as a defence or support - in and of itself - should legal action be taken.
Competent legal and building professionals should be asked to advise in Real Life with rights to inspect and issue reports on the matters at hand.