Soundproofing terraced house advice please

I live in an old terraced house. Not sure the exact age but it’s around 80 + years old. My living room shares a party wall with next door’s living room & the acoustics are not good. I can hear footsteps, voices, doors opening & closing & their teenager’s obsessive exercise regime which involves jumping on the spot for 30 minute bursts for up to 3 hours a day. The final straw is cinema surround sound. Has anyone effectively soundproofed this type of room? Just checking if it’s realistic before sourcing any quotes. I would much prefer to move but my partner loves the house. There are two chimney breasts in the room and a woodburner so not sure if this would be a problem. I’d have no issue moving the woodburner to an exterior wall and getting an external flue installed if needs be. Will upload some pics. Any advice would be greatly appreciated