Strategies to Overcome LinkedIn Connection Request Limits

Hello Everyone, has anyone faced the problem of limitation on adding linkedin account? I have a sales folk working for US country and database is crossing 100K, now to setup the linkedin outreach in tools like woodpecker, supersend, reply.i o, it is not working smoothly. If 3K clicks the link, we want to send linkedin connection request, message. And, here, linkedin has only 100 request per week and have only 1 linkedin account for the sales folk. The LinkedIn account should be same, not of others. How to tackle this problem? Does anyone has solution for this?