In short, the body CAN produce antibodies against antibodies (although it is not desirable and is a form of autoimmunity).
This happens e.g. in rheumatoid arthritis (see https://en.wikipedia.org/wiki/Rheumatoid_factor); RF is an autoantibody against Fc portion of the immunoglobulin.
Antibodies against other antibodies can also be produced by one species against another's antibodies (e.g. anti-rabbit antibodies), which have applications in biomedical research. Production of antibodies against another species' antibodies is also a potential adverse reaction in monoclonal antibody therapies (when using antibodies originating from another species, e.g. mouse; 'humanising' the antibodies reduces that risk).
The question arises, why this does not happen more frequently. For simplicity, I will continue to focus on B-cells (and antibodies, rather than T-cell mediated immune responses). The key is to understand the process for mitigating self-immunity, in general, with a few points that might be antibody-specific.
The journey of a B-cell goes from bone marrow (HPSC > pro-B-cell > pre-B-cell) via mature B-cells (in peripheral circulation, tissues and lymph nodes), first naive, then activated, to plasma cells. The key points for preventing autoimmunity are:
BONE MARROW: VDJ rearrangements. This is antigen-independent. There is negative selection too: B-cells whose receptors are bound to an antigen undergo either receptor editing, apoptosis or anergy (to prevent auto-immunity).
The limitation here is that B-cells are only exposed to limited number of antigens available in the bone marrow. However, because of access to blood/serum and bone marrow containing plasma cells (up to about 3% bone marrow cellularity), it is reasonable to expect that developing B-cells encounter immunoglobulins. As a result of this, in theory there should be no cross-reactivity to antibodies, or at the very least the constant antibody fragments.
(Note that some B-cells get activated and become plasma cells via interactions with T-cells outside of germinal centre, but these are thought to be more important for fast immune response, and generate more short lived cells)
GERMINAL CENTRE: somatic hypermutation (SHM), isotype switching and affinity maturation
After encountering an antigen (in amount meeting a certain threshold), B-cells become activated and migrate to primary follicles and form germinal centre, where they become centroblasts and centrocytes. There, they depend on interactions with follicular dendritic cells and T-follicular helper cells to undergo the above processes. All these events can (in theory and in practice) cause the previously non-self-reactive B-cells to become self-reactive. This is to some degree filtered against. The key points here are:
- there needs to be sufficient antigen (that the B-cell has good affinity for) to allow the B-cell to survive; it is quite unlikely that the B-cell will have a good affinity for a completely new auto-antigen
- the process needs to occur in the right context (antigen alone is not sufficient), with the right support (i.e. FDCs and TFHs), for example co-receptor binding needs to also occur, complement complexes will be present etc. Usually the antigens are displayed by FDCs in the form of immune complexes, which were delivered to them by circulating macrophages.
- in general, there is an excess of rapidly proliferating and mutating activated B-cells, that need to compete for a limited amount of antigen, so only the best B-cells are selected (that can bind to the antigen best). This, for example, means that a B-cell with weak affinity to a (novel auto-)antigen not displayed by FDC will be less likely to succeed than one that has a strong affinity to the (non-autoimmune) antigen on the FDC
Finally, note that antibodies are secreted by plasma cells (i.e. the end stage in the differentiation of B-cells). The earlier stages have instead B-cell receptors, which are membrane-bound immunoglobulins (i.e. antibody on the cell surface).
However, in case of high rates of apoptosis and inadequate clearance of apoptotic debris can increase the chance of autoimmunity developing...
Some background:
https://pathologia.ed.ac.uk/topic/the-germinal-centre/
Basics of germinal centre
Vinuesa, Carola G., Iñaki Sanz, and Matthew C. Cook. "Dysregulation of germinal centres in autoimmune disease." Nature Reviews Immunology 9.12 (2009): 845-857.
https://doi.org/10.1038/nri2637
A relatively aged, but quite informative article on germinal centre in autoimmunity