The short answer is use MSAVI early in the growing cycle, NDVI in the middle and NDRE late in the season. Each index saturates at around 0.8, displaying a basically solid block of colour. When that happens, it's time to move on to the next index.
MSAVI
Use MSAVI from emergence through to canopy closure; in areas where vegetation is sparse; and areas with extensive exposed soil surfaces (to detect summer weeds for example).
NDVI
Use NDVI for medium density vegetation such as mid-season cereal crops.
NDRE
Use NDRE for when NDVI has become saturated above 0.8. Late season cereal crops, high biomass crops such as sugar cane, and permanent tree crops are better suited for NDRE.
Read more about NDVI, NDRE and MSAVI :