This is just my opinion :
At the end of the day, all economic systems deal with the facilitation and distribution of power. It may sound a bit Marxian, but its what I genuinely believe to be true.
The concept behind the antithesis of 'Capitalism' was, naturally, the destruction of power structures. Its opponents, and its very creator in the Wealth of Nations, viewed the system of Capital with varying degrees of contempt. It [Capitalism] was borne out of a need for social egalitarianism during the pinnacle of the European Enlightenment. The tenuous and nuanced relationship, they correctly pointed out, was the means to understanding what an "equal" society would not only look like, but how it could be achieved.
In regard to egalitarianism, the concept has been inextricably bound by perceived and real oppression. Be it the oppressive slave owner, feudal lord, or capitalist, the 'revolutionaries' would view their system as innately unjust, prompting an attempt at its overthrow. All oppressed of all societies are, as the indication dichotomizes, beholden to their oppressors. They, eventually, view the system as unjust, or unequal, and so begins the revolution.
The reason I say all this is because all socio-economic systems have one distinct characteristic. For the established theory, its the maintenance of the status quo, of the power structure through which power is derived. For the heterodox theory, however, the established class is condemned and branded as oppressive (rightfully so, in my opinion).
The burghers viewed the aristocracy as oppressive.
The social egalitarian Enlightenment thinkers then viewed the burghers as oppressive.
Even within feudalism itself, the lords felt threatened and oppressed as the central authority of the king came to fruition. In the end, all socio-economic systems revolve around the same concept, the same struggle. The struggle for egalitarianism and vehement opposition to oppression. Even Gandhianism revolved heavily around the oppression the British had wrought on the Indian sub-continent.
Every power structure is oppressive by definition. As such, there will always be critics of the entrenched echelon. In that, any and every socio-economic system is manifested out of the will of the oppressed, to overthrow the oppressors. Marxian Socialism never came before Capitalism.
So, to conclude, the "third interesting economic system" must be manifested out of the detractors of the established system of power. With that, the possibilities are endless because there have always been power structures.