Short answer: Almost impossible, we were kinda doomed since the Oil Crisis, and later, the crisis of the 90's.
Long answer: maybe, if you manage to make the National Democratic Front (an electoral coalition that included essentially most if not all leftist and center-leftist parties and organizations in the country at that time) to win the elections of 1988 to avoid the rise of neoliberalism in the country and maintain some sort of a welfare state/social democrat form of capitalism.
The biggest question you need to answer yourself is: considering that the NDF wins, what now?. How Cuauhtemoc Cárdenas (the presidential candidate of 1988) will deal with the economic crisis, including inflation and the excessive dependence on oil; how the coalition will manage to work together, if they can work together in the first place; or what will the attitude of the technocrat opposition (the PRI), the conservatives (the PAN), the marxist guerrillas (the FLN) and the nascent indigenous movements, towards the NDF government; etc.
You can't dismantle either the PRI or the PAN since the former one is literally the Party of the Revolution, so even if they have abandoned their nationalist revolutionary stance, they have legitimacy. The PAN is a christian (catholic) party, and most of the population is catholic. Take that into account.