Yeah, but like I said, you’d still be bound by the rules for your canonically enrolled church.
In Orthodoxy say I’m going to a Serbian parish (which I am) which is on the Old Calendar (which it is). If I go to the Greek parish down the street on the New Calendar I start fasting by the New Calendar. In other words the major Feast Days change, the start of Fasting seasons change, etc. That’s ok, I just start fasting when everyone in my Greek parish starts fasting. I’ve known at least one woman who did all of exactly this.
But if I’m a Serbian Catholic (don’t think that’s the actual term but close enough) and I start going to a Byzantine Greek Catholic Parish, I am still bound to follow the fasting schedule of the Serbian Catholic church. If I go to a Latin parish I have to observe the midnight to Eucharistic fast on Sundays even though almost nobody else is in my parish. I still have to fast Wednesday and Friday and, from what I’ve heard, the major feasts are Holy Days of Obligation in Eastern Catholicism, so I’d have to attend Mass on those days even if the rest of the parish isn’t celebrating the feast on that day.
It’s just a difference, like the OP was asking about.