Last time I looked at Trinity Seven it was attempting something like this. There's a clear harem of the MC and the seven girls with one pair clearly standing above the rest. But flash backs confirmed it was always him and the seven together (it's a reincarnation plot). It's clearly building relationships between the seven girls who aren't already close and everyone was helping to improve each other and growing as a group. It has been a while though so I'm not sure if they manage to actually carry on that positively.
I've seen 2 anime actually pull of polyaamory reasonably decently. Interestingly both are female centered mecha shows. Cross Ange doesn't hit it as well, but the relationship only really comes right at the end and it is a fanservice series, although surprisingly hard hitting for a fanservice series. While the main pairing is obvious with Ange and Tusk and is built up from their first meeting, towards the end it starts becoming obvious Hilda is also interested and it becomes polyamorous. And despite it being she's mostly interested in Ange, she has shown enough interest in Tusk to make it believable.
Rinne no Lagrange is aimed at an older audience and so it might not be surprising it handles it a lot better. The relationship is built up as romantic from about the midpoint of the series and does a pretty good job of building it naturally and believably from uneasy alliances to friendship to romance. It is adorable and soft and belieable and the drama and relationship issues come from external forces (aka that interplanetary war going on) rather than relationship melodrama over who's got one person's affections more ect.
It's entirely unobvious at the moment apart from the fact that they're all on the cover together, because it's only just started, but Where The Sky Lies is planned to head in this direction with Francis, No1 and No11. It's pretty slow burn and builds generally from just being around each other rather than any sort of pushed romance. I'm aiming for it to be pretty natural and and it's basically there emotionally long before there's any real acknowledgement from the characters because I'm a sucker for "it's so obvious how do they not see they're in love?" (how successful that will be is a matter for the future).