We don't push Agile, we expect clients and Teams to pull it.
In our fairly sizable yet chunky enterprise, we have a community of Agile champions. Our role is to help kick-start teams and organizations on the path to using Agile methods well. That includes indoctrination in various thinking, organization and action tools, as well as ongoing coaching to ensure a continuous improvement atmostphere gets established and then sustained.
We start by forming communities of practice that include leaders at various levels, and involve the Agile coaches and mentors that will work with the Teams themselves. That works very well where leaders respect people and treat them accordingly. In situations where some managers view individuals as fungible resources, we politely say our goodbyes and if needed put in a word with some leaders further up the org tree - we're fortunate to have a sensible CEO now and some wise Vice Presidents (of various flavors), so that helps a lot.
One interesting aspect is that we can help any and all teams improve their thinking and habits, regardless of the flavor of work process they use. Using Agile thinking is not like flipping a switch - Friday you were in a Waterfall Team, Monday you're in an Agile Team. It takes time and a fair amount of study for folks to adjust their perspective. It takes practice for people to master new habits. It takes trust for them to volunteer their better thinking and take charge of their own work processes. Communities of practice make the journey of continuous improvement sustainable.
So, in some of our larger organizations, we start by gently and progressively improving all flavors of work processes. Once a culture of continuous improvement takes hold through its habits of inspection and adaptation, work processes can shift to their optimum spot in the spectrum as driven by client needs and investments.
We also always start by saying "Why do you want to use Agile? Using Agile for Agile's sake isn't a good enough reason". That leads to some very interesting conversations with various leaders and managers. In short, we either reach win-win and proceed, or no-deal and go for the next opportunity.