Are the effects additive or subadditive? In many ways, rapamycin acts like a CR mimetic, but even CR can only go so far.
To clarify; administration of rapamycin (a drug) to lab organisms (including mice ) extends lifespan. Similarly, restricting the intake of nutrients to the minimum without causing malnutrition also extends lifespan in lab animals (including primates ).
Rapamycin inhibits the mTOR pathway (mammalian Target Of Rapamycin) - specifically mTORC1 (Complex 1) - which influences protein synthesis, autophagy and inflammation (among others). Upstream factors of mTOR include nutrient availability and insulin signaling (see "Deconvoluting mTOR biology" for good review ).
It has been hypothesized that the lifespan-extending effects of caloric restriction (CR) are mediated by mTOR (one can see why - mTOR is affected by nutrient availability). In fact it may depend on the method of CR;
Greer et al  report that different methods of CR in C.elegans, for instance feeding them a diluted food source, or conversely feeding them on alternate days, do not necessarily require the same genetic pathways. Not only this but CR combined with a genetic mutant (eat-2) have additive lifespan-enhancing effects.
So whilst the evidence is not concrete, and I look forward to other studies in mammals similar to the one by Greer et al, it looks as though rapamycin and CR have similar but not exactly the same effects on lifespan; rapamycin specifically inhibits an individual pathway which is involved in many processes, and some of its effects are not necessarily desirable (e.g. rapamycin inhibits the immune system ). On the other hand, CR (most of the different types) seems to be mediated by mTOR - this difference is critical: mTOR is not necessarily inhibited by CR, it is just required for its effect.
Therefore combining rapamycin and CR is unlikely to have an additive effect as rapamycin may override any influence CR has on mTOR signaling, but I have not seen a study in which this has been tried. Combing different methods of CR (or developing drugs to do just that) may well have additive lifespan-enhancing effects.
- Harrison DE, Strong R, Sharp ZD, et al. Rapamycin fed late in life extends lifespan in genetically heterogeneous mice. Nature. 2009;460(7253):392-5.
- Colman RJ, Anderson RM, Johnson SC, et al. Caloric restriction delays disease onset and mortality in rhesus monkeys. Science (New York, N.Y.). 2009;325(5937):201-4.
- Weber JD, Gutmann DH. Deconvoluting mTOR biology. Cell cycle (Georgetown, Tex.). 2012;11(2):236-48.
- Greer EL, Brunet A. Different dietary restriction regimens extend lifespan by both independent and overlapping genetic pathways in C. elegans. Aging cell. 2009;8(2):113-27.
- Thomson AW, Turnquist HR, Raimondi G. Immunoregulatory functions of mTOR inhibition. Nature reviews. Immunology. 2009;9(5):324-37.