The Asian Development Model is certainly different, but not an entirely different option. It is still grounded in free market ideology.

Japan definitely made a run with what has been called state development capitalism. In Japan the state worked closely with companies to plan, but not command and control, outputs. Quotas were used, but with direct consultation with business elites.

Korea has done similar, building up giant business conglomerates called chaebols. Korea had a fairly centrally planned economy based on government-directed investment. This changed at the turn of the century when Korea started to reform and sought a more market-based approach after the Asian financial crisis.

There are not really alternatives to but instead a mix of state-planned/directed economies and a more market based approach. An economy has to know what and how much to produce. This can either be done by listening to the market, the state, or a mixture of the two. Outside of those two, it becomes problematic to find a way in which an economy can come up with answers to basic questions like resource allocation and supply.

Perhaps a better way of formulating your question would be to ask about alternatives to socialism and capitalism, as opposed to communism and capitalism, as there were quite a few governments around the world (eg. India until about 20 years ago, Tanzania under Nyerere and his philosophy of 'African Socialism', Nicaragua under the Sandinistas) that adhered to some form of socialism as their prevailing ideology, but not to communism as such.

Other major ideologies included Islamic theocracies (modern Iran, Afghanistan under the Taliban) and Baathism/pan-Arabism (Egypt under Nasser). There was also Gaddafi's Libyan Arab Jamahiriya, which included elements of both pan-Arabism and Socialism combined with a form of totalitarianism disguised as direct democracy.