Do cutoff ranks change between rounds?

Yes. Closing ranks generally become more relaxed (numerically larger) in Round 2 and the extended round, because candidates who got seats elsewhere (for example through JEE or COMEDK) exit and free up seats. However, for the most sought-after college-branch combinations the movement can be tiny or zero. Where we have per-round files (2018 onward for most years), you can compare rounds directly.