How man scrum teams does my size organization have?

I don't believe that there's a sweet spot for Scrum teams at the organizational level. The biggest limiting factor is most likely going to be organizing your teams around products. In the most basic case, where you have one team per product, it's pretty straightforward. The bulk of the scaling frameworks that I'm familiar with scale well to between 2 and 9 teams per product, but you'll probably need some different structures forming beyond that. There are some different ideas around what constitutes a product or a portfolio of products and focusing on defining product boundaries and having knowledgeable, empowered Product Owners and any necessary supporting staff in product management will probably be one of the biggest things to overcome.

My opinion is that there is no such thing as a "sweet spot".  An organization should have enough teams to get the work done on a consistent and ongoing basis while continuously providing value to the stakeholders.  The number of employees in the company and the rate of growth have no bearing on the number of Scrum Teams you utilize.  

However, if those 330 employees are all on the 3 current teams, that changes my answer in so many ways.  But I am going to assume this isn't the case. 

Is there a sweet spot when it comes to the number of scrum teams at an organization level?

Probably, in so far as there is likely to be a constraint determined by organizational dependencies.

• How are the dependencies teams face — when trying to develop and integrate releasable increments each Sprint — currently visualized and managed?
• What is the organization doing to descale the integration challenges teams face, so they have fewer dependencies to navigate?