Tibet is a Mahayana country, and the Mahayana expanded the Brahmaviharas to limitless/immeasurable love, compassion, joy and equanimity in their training in Bodhicitta. The meditations have an expansive quality and bring one from, for example, metta (maitri) towards one person or a select group, to all sentient beings throughout all world systems. Thus, the mediation on equanimity can come first or last, and is a part of all the other three. There are practices one can do on each one, but generally they balance each other out, so they are done as a series. They are generally called the "Four Immeasurables" in English. Pema Chodron I believe has a book on these, and I'm sure others do. Although the translation it is a very dated, the greatest Nyingma scholar yogi, Longchenpa, taught how to do these practices in either Vol. 1 or 2 of a translated text called Kindly Bent to Ease Us, translated by Guenther a long time ago.
Each Tibetan lama emphasized Mahayana training to a greater or lesser degree. When I practiced the Longchen Nyingthig foundational practices, I spent a significant period of time cultivating the four immeasurable as a practice while I was focusing mainly on the Bodhicitta aspect, following Longchenpa's advice. As I recall, I did all four in a session to a greater or lesser degree based on time and what felt right. I bet the Gelugpa's focus on this a lot, because they generally emphasize a long period focusing mainly on the Mahayana. The Sakya, Nyingma, and Kagyu Schools generally try to move people along into the Vajrayana because it is viewed as a swifter path to enlightenment. But, each to his own!