Just about every question about words here on iTalki involves Latin words. Why is that? Lest you believe that all English words come from Latin, that is not the case. The best English words come from the northern countries: Germany, Scandinavia, etc., but the complicated and sophisticated words come from Latin. One of the secrets to speaking English well is to make more use of the non-Latin words. Using lots of Latin words can make you sound sophisticated, but also pedantic.
For both "repose" and "repast", I find the interpretation as "back" or "again" more convincing than the idea of an intensifier. The Latin roots are so obvious. The Latin roots of "repast" mean "graze again". Isn't that beautiful!
All of the words below are Latin based. In most cases, "re" means "back" or "again". But not always. For instance, "reify". It comes from Latin "res" which means "thing". So "reify" means to consider as a thing.
revolve, reprise, report, reify, receive, repel, return, remain, reject, retain, retire, retract, rebound, revenge