[рони]

Castromen,

var data = {
	"user 1": {
		company: 'Рога и копыта',
		name: 'Александр',
		projects: {
			projectID1: {
				role_right: 0
			}
		}
	},
	"user 2": {
		company: 'Копыта и рога',
		name: 'Петя',
		projects: {
			projectID1: {
				role_right: 0
			}
		}
	},
	"user 3": {
		company: 'Копыта и рога',
		name: 'Василий',
		projects: {
			projectID1: {
				role_right: 2
			}
		}
	},
    "user 4": {
		company: 'Копыта и рога',
		name: 'Иван',
		projects: {
			projectID1: {
				role_right: 1
			}
		}
	}
};

var newData = Object.values(data).reduce(function(object, user) {
    var obj = {
            role_right: user.projects.projectID1.role_right,
            company: user.company,
            name: user.name
        },
        item;
    if (user.company in object === false) {
        item = {
            title: user.company,
            data: [obj]
        };
        object[user.company] = item.data;
        object.newData.push(item)
    } else {
        var arr = object[user.company];
        for (var i = arr.length - 1; i ; i--) {
            item = arr[i];
            if (item.role_right < obj.role_right) break;
        }
        arr.splice(++i, 0, obj)
    }
    return object
}, {newData: []}).newData;

console.log(newData);