first caller gets muted when a second call comes in

1st suggestion
Sounds like it is working okay for you and only 1 employee is affected. Might be worth it to compare the Audio settings in the app between you two. Make sure your employee has the exact same audio settings as you. 

2nd suggestion
If above doesn’t help then you can trade headsets with your employee as a test. This isn’t about solving the issue, but about collectin as much info as possible about the issue.

3rd suggestion
Reinstall app / try the web app instead of the desktop app / try a different PC. - again, this is just ruling stuff in or out.

and a final nuclear option
Settings > Phone > Call waiting > Disable it to prevent 2nd calls from ringing if you are already on an active call.

I am experiencing this same issue. Was there a resolution to it? We tried a new headset, reviewed all the settings, reinstalled the desktop app, and even tried just using the web browser version (suggested by RC tech support) but the issue is still occurring. With the exception of disabling call waiting as we get a high volume of calls that makes this option impossible. 

I have also had this issue, many of my collogues do too.  I have uninstalled and reinstalled the app multiple times, the issue is still not resolved. It happens with the actual phone, as well as the cellular app.

I will not disable my call waiting, as sometimes I need to let someone off the line to respond to a more pressing matter.

It seems that all the options listed are not solving the problem.  Maybe this is on RingCentrals problem to solve

….it’s not a bug, it’s a feature. 

I can understand that the first call gets muted while the new call is coming in, but once the call goes to voicemail, the first call should return to regular volume, it does not. It stays muted for the duration of that call, that is a terrible “feature” in my opinion.