Where is this plant located? What conditions, sun, shade. Could you manage a clearer photo that shows leaf veins?

I'm in Southern California - zone is 10a, but I'm surrounded by 9b zones.

The one growing up the kumquat tree is full sun.

The one under the orange tree is shaded by the tree until maybe noon, then sun for the next 4-5 hours probably. The one under the orange tree does get some regular watering. The one by the kumquat tree gets zero additional water. So, that it's doing good right now in SoCal, in direct sun for one of them, seems like it's very drought tolerant, so maybe has a deep tap root?

Does the plant have white, milky sap?

I didn't think so, but now that you asked, I just went out and checked, snapped a portion of the vine,, and yes - a bit of white milky sap did come out.

Maybe Matelea parviflora? The leaf bases,(ears) are mostly cordate, but variable. Not sure about petiole length matching tho? Maybe 1 more clear picture like the 1st photo showing vine, leaves, arrangement?

Thanks - I think you got me pointed in the right direction with that. I'm thinking it might be either Gonolobus suberosus or Matelea carolinensis. I'll watch for flowers, and maybe that will narrow it down then. Sounds like in either case it could be toxic to my pooch if he were a plant-eater. But he's not adventurous to where he'd be eating it. Sounds like it's probably good for monarchs, so I'll leave them be for now, and might later do something with them if they seem to be taking over too much.

Matelea caroliniensis normally doesn't occur east of Texas, but it could have been introduced. There are also 4 species of Funastrum and Cynanchum louiseae in your area. Gonolobus suberosus a definite possibility.