I know the Launchpoint service will only let you connect 1 of each service, so you can only have a single LinkedIn connector as far as I'm aware.
I would try giving the integration user (i.e. the user who's credentials are used when setting up the Launchpoint matched audiences service) access to multiple LinkedIn accounts. When you push your lists via AdBridge, there is a drop down that lets you pick to which account/list you want to send the audience. I would suspect that in that drop down, if your user has access to multiple LinkedIn accounts, you'd be able to direct the audience to the appropriate account, but I have never personally used multiple in my own instance.