Dropbox and Box employ a bit of a hybrid model.

For SMBs, there's a self service model that's low touch but for enterprises, the sales + customer service is very high touch and requires a lot more customization.

BI tools such as Periscope, Looker, Mode, Tableau, etc are also a bit of a hybrid. Usually starts off with an individual playing around or looking for a tool (pretty self service), but a full company deployment is much more hands on and high touch.

Following the framework that Patrick provides, odds are that any company that has "sales engineering" or "integration engineering" for a SaaS will likely be high touch (unless they're doing it wrong =D)

There are a lot of small companies offering that - a mix of SaaS and custom development.

In a previous company, we built a SaaS platform (based on Odoo, a kind of semi-open-source web version of SAP) which allowed clients to purchase changes to any part of the application. Unlike in a typical SaaS, each client had its isolated copy of the app/database/etc (though all running on our cloud), so they could change anything. Some changed nothing, others have whole new components and business flows.

I would consider NewRelic, AppDynamics and other more expensive APMs high touch.

High touch SaaS sees much... much.... much... less benefit from marketing. So many don't market themselves as often, or market in specialty places. Salesforce isn't even that much of a household name.

Qualys