Being in two relationships, I started with the aim of equality, which I largely (subconsciously) equated with sameness. Not maybe as "everything has to be the same right now" but as "the eventual aim is symmetry". I think this was valuable at the beginning of poly in terms of being open to changes. However, at some point it started to become increasingly clear that the aim of symmetry was not always something that aligned with what the people involved actually wanted. Also, it seemed that the aversion towards hierarchy (plus some internalised relationship-escalator-as-measure-of-serious-relationship assumptions) was something that caused pressure towards equality. So, the aim of equality as symmetry moved aside, and was replaced by more flexible decision making based on what all want.
I think there are some aspects that have been incredibly helpful. Firstly, I don't view my poly life as something separate from other aspects of my life. Secondly, I used to have an autonomous relationship when monogamous, and I have not changed this since becoming poly. These tie in together, and I will try to illustrate.
When monogamous, I would make decisions concerning the ways in which I spend my time autonomously. Obviously, I want to spend some time with my partner, so that fact will be factored into the decision-making, along with any preferences he has expressed in the past. But if I want to see a friend, I will make plans with my friend and let my partner know about it. If he has any wishes, he is free to express them - e.g. "I have Sundays off and would like to see you then" - and I am happy to consider them in the future, but I will not cancel plans with other people once I've made them. When opening up, there is no reason to change this method - i.e. when making plans with another partner, I will not start asking for his permission, or even checking with him in advance, any more than I do when I'm making plans with a friend. He is as free to express his wishes as he's always been, and I am happy to take them into account in the future.
Poly is not separate from life. Romantic relationships are relationships. I will make my own decisions autonomously as I've always done. If my partner expresses wishes, I will consider them based on their reasonability, validity, and my own judgement; not based on some hierarchical status. I would not cancel plans with a friend simply because my partner asked me to, and I will not cancel plans with a newer partner because older partner asked me to. I would not give up a friendship simply because my partner wants me to or doesn't like my friend, nor would I break up with a person for those kind of reasons. You get the picture. None of these situations have ever happened. I doubt any of them will ever happen, because there is a mutual respect for each other's autonomy, which recognises that unreasonable demands don't become any more reasonable in romantic relationships. That is not to say that we are above that - more that we all know ultimatums etc. would not be met with compliance, because, eventually, none of us want the kinds of relationships where they are used.
Egalitarian relationships are a process. We have established a relationship life and routines that work for us. However, there is a need to remain open to change in order to take into consideration potentially changing wishes. That is the key; consideration. Doesn't mean you need to change everything, or accommodate everything your partners want, or compromise everything. It means to take seriously the wants and wishes of all people involved, whatever they are and become.