Leveraging LinkedIn Networks for Team Collaboration in Sales Prospects

Any best practices / tools on leveraging a whole team's LinkedIn networks to finding best way into a corporate prospect? Knowing someone at a company who can intro you to the right person at that firm can be a huge benefit for enterprise sales. With our sales team of 30 people and a target account list for everyone, it can be tricky to keep an overview of who of your colleagues could help you with that intro. The LinkedIn privacy export of connections can be one way to get the connections but having everyone do that and consolidating it is quite tedious. Do you have any recommendations how you can easily import a whole team's connections and finding the best way in? Maybe there are also free tools?