However, one form of market socialism I believe could function as a very real template of reform was proposed by mathematician by the name of Dr. David Schweickart. He proposed a model of "economic democracy" not too dissimilar to the current economy we live in except for several key defining features:
1) A national public bank funded by a capital assets tax on all businesses. The tax would replace all business taxes and is a flat rate one. The money would then be dispersed to each regional, sub-regional, and local branch of the bank on a per capita basis to be invested into the economy. The tax, essentially, is the manifestation of the idea that capital assets are collectively owned by society and that a business "rents" it for its own purposes.
2) The bank will act as an agent to fund the start-up enterprises managed by the workers themselves, a labor co-op, and the bank can also offer financial advice as well as buy out existing firms to be re-organized into more labor co-ops and grant more funds to existing labor co-ops.
3) All of these enterprises will be free to sell their products and services in a market mostly free of government price controls, and prices are determined by supply and demand.
The effect of this, hopefully, is an economy that is essentially split into two sectors: The co-op sector, and the traditional private sector. Businesses in the two will compete amongst themselves and against each other, and the key here is that workers would have a real choice between working collectively to enjoy the fruits of their own labor or selling their labor to a traditional capitalist for whatever they can get.
In time, it is hoped the co-op sector would grow to match or surpass the private sector in terms of output and numbers and would become the driving force in the economy instead of the capitalists. If this is achieved, you will be one step closer to eliminating things such as hunger, disease, poverty, and homelessness.