We have and idea, which significantly simplifies access to messy and diverse knowledge bases and complex intranets. We're still trying to evaluate it, but it's already clear, that it gains value as the size of the company (customer) grows. Smaller companies don't have that much mess and probably won't pay for any solution for that. However, I'm pretty sure they would be willing to try it for free and free users also have value as they form a community around the product. So, my question is how good is the model when most of the product is open source (e.g. community edition) and enterprise version, with advanced features, only relevant for big companies, is sold for a fee. Without any experience it looks attractive, but what are the downsides? What's the investor opinion on such model? It seems like such approach would delay the first revenue and require significant engineering effort from start. Would it be even possible to raise money for it?
There's no such thing as "semi-open source" It either is open source, or it isn't. The nature of open source makes it so that everything built upon it must be open source according to most of the open source licenses.
The idea you're proposing is very popular and used all the time by big successful companies. See Redhat, Atlassian, vTiger, SugarCRM, WordPress (Automattic). The key is offering value on top of the open source free/community package. The value for an enterprise would be your service and expertise in maximizing the software, professional support, or customizations for them, or even hosting it for them.
The upsides of doing it via open source is that the small companies that won't pay to license or service fees will customize some of it and hopefully contribute back to the software which will make it stronger for everybody. And as they grow they might eventually need your services or paid offerings.