Class-switching is the result of further rearranegment of the gene segments in the heavy chain locus. A number of C gene segments are excised, with the result that one of the downstream C gene segments is now transcribed along with the VDJ unit. This means that when a B cell undergoes class-switching, its antigen specificity is unaltered. Sequential class-switching can theoretically occur. Thus, a B cell could switch from IgM production to IgG2b production and subsequently to IgA production.
Sequential switches can only occur in one direction.
When a B cell is activated in an immune response and becomes a plasma cell, the antibody it produces is secreted rather than membrane-bound. As stated above, fully mature B cells express both IgM and IgD on their membranes. All of the IgM and IgD on their membrane has the exact same antigen specificity. Immunoglobulin genes are only transcribed to any appreciable extent after gene rearrangement has occurred. The answer concerns the relative location of enhancer, silencer and promoter regions in the Ig loci.