The overarching goal of communism is for laborers to own the means of production instead of an owning/capitalist class. Employee owned businesses are the realization of communism within a capitalist society.
It seems to me that most communist organizations in capitalist societies focus on reform through government policies. I have not heard of organizations focusing on making this change by leveraging the capitalist framework. Working to create many employee owned businesses would be a tangible way to achieve this on a small but growing scale. If successful employee owned businesses are formed and accumulate capital they should be able to perpetuate employee ownership through direct acquisition or providing venture capital with employee ownership requirements.
So my main questions are:
- Are organizations focusing on this and I just don’t know about it?
- If not, what obstacles are there that would hinder this approach to increasing the share labor collective ownership?
Look for Wohnungsgenossenschaft or Wohnungsbaugenossenschaft. They are relatively common in Germany and Austria; Vienna is an example where the majority of flats are owned by such cooperatives. In Hamburg roughly 14% of all flats in the city are being provided by cooperatives which has huge advantages for those who get to become members.
All sources I know are in German language so if you want to read further just go for these texts and translate them into your mother tongue. Maybe start with Wikipedia:
https://de.m.wikipedia.org/wiki/Wohnungsbaugenossenschaft