When Springsteen toured with The River - a double album - in 2016 celebrating its 35th anniversary, he played it in full - on the first US leg, and at European shows where he had multiple night stints.
Seen him to do Born To Run, Darkness on the Edge of Town, and Born in the USA. He's also done Greetings from Asbury Park, and The Wild, The Innocent and The E-Street Shuffle over the years. (The latter in Australia, and he's only done it twice IIRC - the other time in NYC).
Album shows are great, IMO. I've only seen him do it, and his catalogue is deep enough to still get plenty of everything else.