It used to be that reapportionment, including setting the size of the House and determining which method to deal with fractions was done after each Census. Congress was unable to decide after the 1920 Census, so in preparation for the 1930 Census, they set a fixed number (435) to be that done for the 1910 Census, and fixed the method to apportion that number. Significantly increasing that number would mean either building more House office space, or reducing the amount each Representative gets (and thus the amount of Staff). Actually, giving Hawaii and Alaska Statehood helped slightly as it cut the number of territorial delegates by 2. No one has been willing to reopen the can of worms since then.
I met the Architect of the Capitol about 20 years ago. He said that it would not be difficult to expand to 600 members (think about occupancy during the SOTU), but more than that would start to run into space problems.
Back in May 2018 I did a series on how the chamber would expand based on the rules typically used to determine expansions before 1920.
Yeah, the chamber itself could handle more members, but it's not as if there's unused office space, and Congresscritters enjoy their staffs and their creature comforts. They've already freed up space in the three main buildings for member offices by relegating committee and support staff to the unconnected Ford and O'Neill Buildings. I suppose they could relocate the Bartholdi Fountain and build a fourth building for member offices where Bartholdi Park now is, but even that dreary expedient wouldn't add that much office space for members.
