ワードアップ英会話 WORD UP ENGLISH CLASS | 日記 | Idioms: "have a lot on (my) plate"

To have a lot on your plate can just mean you actually have a lot of food on your plate, like what most of us do at all-you-can-eat buffets.

But as an idiom, if you "have a lot on your plate" it means your schedule is really busy or you have a lot of things to manage.

Here are two examples:

Bobby: Why didn't Rosa come to the barbeque?
Donna: I don't know, but I heard she's busy with work and school, so she probably just has a lot on her plate right now.

-OR-

Reika: Are you okay? You look really tired.
Demitri: Yeah, I'm all right, but I guess I'm just a little stressed out because I have a lot on my plate these days.