Also google "somatic hypermutation". That multiplication process for B cells is inexact, and introduces mutations into the DNA (and therefore structure) of its children. There's a process which indicates whether any of these new antibodies binds better than the original one, which becomes a new candidate for multiplying.

There's fairly recent technology to sequence these antibodies en masse, which gives you a whole load (~10^6) of these antibody DNA sequences. It's a fascinating and frustrating exercise to try and reconstruct the mutation history and families of related cells from this data.