Usage of いけれる (SPOILER! 人は見た目が１００パーセント ep.9)

[Saruko]

So last night I randomly put on the drama 人は見た目が１００パーセント and found it surprisingly easy to follow, except for the very end of the episode which I was trying to understand more carefully since it seemed important for the plot and character development. They meet for a date. After the guy (Sakaki) says “you and the girl you saw me kissing are both my girlfriends; is that not allowed?”, and she splutters something unintelligible, this is what I heard (transcribed to the best of my ability):

僕は城之内さん（じょうのうちさん）のことが全部行けれるつもりですよ。
(she hears him say the following lines in a flashback)
恋人として、お互いのいいところも悪いところも全部行けれて認めあってともだと思うかも。

だから、城之内さんは今のままの城之内さんにいいんです。

だから、僕のことも全て行けれて欲しいんです。
(back to the present)
僕は城之内さんのことが本当に好きですよ。

ずっと大事にしたいと思っています。

だから、これからも一緒に行ってくれませんか。

My general understanding of this part is that it’s basically a big confession of love that completely dodges the issue of having two girlfriends, but this is the first time I’ve really encountered いけれる and I can’t quite wrap my head around it… Since its used three times here I’d like to try and understand that word. Does anyone have any other examples of this word? Or any insights to share?

[Leebo]

いける can be “to go well” so, いけれる would be “to be able to go well” in that conjugation. Without bothering to read the whole thing, does that make sense?

Of course, you’re saying you don’t have an actual transcript, this is just what you think you heard?

[Saruko]

yeah, this is what i think i heard
so it could definitely be off
something I thought was interesting is that each time the verb is preceded by 全部 or 全て

If いけれる means “to be able to well”, then maybe the first sentence could roughly mean something like “I want to do well by you.” as in “Give me a chance, I’ll make you happy.” ??