I'm not sure that dualist either/or systems really exist. Most economic systems contain elements of both.
One possible example is Sarvodaya in India.
Sarvodaya is a term meaning 'Universal Uplift' or 'Progress of All'. The term was first coined by Mohandas Gandhi as the title of his 1908 translation of John Ruskin's tract on political economy, "Unto This Last", and Gandhi came to use the term for the ideal of his own political philosophy. Later Gandhian, like the Indian nonviolence activist Vinoba Bhave, embraced the term as a name for the social movement in post-independence India which strove to ensure that self-determination and equality reached all strata of India society.
The link;
Gandhian philosophy of sarvodaya and its principles | Gandhi's Views | Articles on and by Mahatma Gandhi (mkgandhi.org)
Uno de los sitemas no capitalistas que existen es la Economía del bien común. Promovida por el economista Christian Felber, se fundamenta en la idea de que la economía capitalista se sustituyese por la economía del bien común de forma que dejaran de primar los valores como el afán de lucro y la competencia, para regirse por los principios constitucionales.
Kibutzim in Israel could be regarded as a different form of socio-economic practice (though I am not sure about the trend of their size and numbers in recent years).
It is called "self-provisioning" (aka 'subsistence economy'), and is being used by millions of people around the world, mainly rural small agriculturalists. Today most have some dealings with the capitalist market, but the primary focus of the participant's economic decision-making is on fulfilling the known needs of the family unit, so that it is non-capitalist in terms of its core motivation. In this economy the rules of supply and demand do not function.
I wonder if the NEP, as envisioned by Lenin, had been part of a longer term plan rather than a short term mechanism to stabilize the economy, and had run its full course, what the outcome would have been.
En las zonas rurales de sur de Tucumán, el oeste de Ccatamarca y el sur de la Rioja, se desenvolvió un modo de producción denominado "comunitarismo rural" que se basó en el uso compartido de tierras, aguadas y bosques por parte delideres rurales que acuerdan un eticidad común en el manejo de manadas y "bañados"....