Considering the Thymus
The thymus is the source of immune cells, but involutes in adults - it shrinks and loses its functionality. Restoring the thymus is one possible way around some of the built-in limitations of the immune system that contribute to age-related immune failure and a shorter life: "Emerging evidence indicates that the immune and metabolic interactions control several aspects of the aging process and associated chronic diseases. Among several sites of immune-metabolic interactions, thymic demise represents a particularly puzzling phenomenon because even in metabolically healthy middle-aged individuals the majority of thymic space is replaced with ectopic lipids. The new T cell specificities can only be generated in a functional thymus and, peripheral proliferation of pre-existing T cell clones provides limited immune-vigilance in the elderly. Therefore, it is hypothesized that the strategies that enhance thymic-lymphopoiesis may extend healthspan. Recent data suggest that byproducts of thymic fatty acids and lipids result in accumulation of 'lipotoxic DAMPs' (damage associated molecular patterns), which triggers the innate immune-sensing mechanism like inflammasome activation which links aging to thymic demise. The immune-metabolic interaction within the aging thymus produces a local pro-inflammatory state that directly compromises the thymic stromal microenvironment, thymic-lymphopoiesis and serves a precursor of systemic immune-dysregulation in the elderly. [This has] implications for developing future therapeutic strategies for living well beyond the expected."
In my limited understanding, it might be easier to replace the thymus wholesale (via an organ printing / implantation strategy) than to figure out exactly what goes wrong with it. In general, I don't think piecemeal replacement of whole organs is a good way to go about rejuvenation absent specific and acute disease, but this may be an exception. It would also provide a good vehicle for the delivery of gene therapies to the immune system that could, for instance, encourage the targeting and clearance of senescent cells.