LinkedIn (both LinkedIn Pages and LinkedIn Ads) limits the way we can add integrations. The reason you might not see the pop-up box reappear after adding your first integration is because you’re still logged into the account you already added (so LinkedIn thinks you want to reintegrate the same account).
1- Sign out from your LinkedIn account in your browser
2- Go into your DashThis account, and click on Add next to the LinkedIn integration.
3- Connect the desired account