What are some suggestions for a community building platform?

Good question and a big question. It's most important to first define what we mean by the term "community building platform". While not clearly stated, I'm going to assume that you mean building an "online community" using an online platform to support it. If understood as such then I am fairly confident that you've come in contact with at least a few online community platforms already - Facebook, Twitter, Snapchat .. to name just a few.

Next item of business is clarifying what it is you would hope to accomplish with any given "online community". There are no shortage of reasons ... for social, business, education, or medical purposes. All viable, all ultimately designed to promote some sort of interaction between "members" .. all needing to be perceived by those who participate (even as lurkers) as having "value".. something that they can both observe and contribute to; offering something that they have difficulty finding elsewhere.  To understand this further, reflect on your own experience via your use of common social media tools such as Facebook or LinkedIn. Why do you invest time and energy into viewing and commenting via such tools? Typically because they are easy to use, easy to share with others, are clear about what one can expect to find on them, as well as safe and providing some sort of "value" that would be difficult to realize elsewhere. 

As for which platform to use - there is no shortage of online community platforms to choose from but it may come as a surprise to learn that the choice of platform becomes less important than projecting a clear purpose and attracting the right members into an online community. That is far more challenging to realize because that involves creating perceived "value" typically accomplished by first ensuring there is an online climate that is "safe, and open" .. engages in the "discourse" unique to the community; encourages exchange, support, and involvement of others - beginners, apprentices, as well as influencers and leaders. For more on this, I would urge you to review the work of Etienne Wenger-Trayner who has made it his life's work to focus on just how to realize online communities.

The concept is to grab people's attention using all the best practices of building community, users never need to log in or register or download anything, and the platform for the manager is sophisticated and smart. Main features: directory, email system with posts/polls/events/files, with analytics and easy follow-up buttons embedded in every communication. All synced together.

Privacy and Innovation and Specialization

I would like to know your definition of community building platforms? Based on my definitiions here are some suggestions.

Blogger Outreach:

GroupHigh

Meetup or GroupSpaces

CRM and ERP:

JiveX

Lithium

Yammer

For Scouting communities use Plancast

On Mobile:

Minsh

Popcorn

Within the education industry, you have Spoke and Edmodo

For offline I suggest:

LEGO Serious Play

Design Thinking workshops

Within the education industry I am very fond of