We've operated a SaaS product for many years and we think our pricing is too low to enable growth. I believe we need to raise our prices on all current customers and not just rely on higher prices for upgrades or new customers only. We're really serving customers and launching valuable features right now and would like to make an announcement in a couple months that the new pricing is going into force. To be fair, we plan on giving customers 60 days to decide if they want to continue service and we don't think there are any comparable alternatives to our service.
Yes, thousands of companies. This answers your social proof question.
However, what you really need to know is that due to price quality effect... it is entirely possible that by raising your prices you may actually increase volume!
I recommend doing a volume hurdle analysis before any decision is reached. How much volume can I afford to lose that the price increase will make up for? Then it is just forecasting what will happen to volume via elasticities.