Latin and the Allative Case

Maybe some of you already know about the "allative case," but I only learned this term within the past year. According to the SIL Glossary of Linguistic Terms, "Allative case is a case that expresses motion to or toward the referent of the noun it marks."

Also from lexico.com concerning "allative":

Mid 19th century; earliest use found in Quarterly Journal Education. From post-classical Latin allativus, designating the case expressing motion to or toward (1826 or earlier; earlier in sense ‘for bringing’) from classical Latin allāt-, past participial stem of afferre to bring to + -īvus.

It seems that Latin might not have the allative case or lost it over time, but the language possibly found ways to communicate similar ideas through merged cases. Early Greek apparently made use of the allative case, which is an extension of the locative case. I guess the difference is that motion towards an object is indicated by the case ending with the allative whereas the five-case system in Greek doesn't always do this explicitly. 

I also read section 427 in Allen and Greenough: it's provides some help. A & G give these examples inter alia for how Latin indicates motion to or toward an object:

bellī, mīlitiae, and domī; terrā marīque is another good one.