You can learn from this article what limitations apply on private and channel sessions.

In case of private sessions:

There is no restriction on the number of concurrent private sessions. However, there is an account-level restriction on the number of new sessions that can be started per minute. A maximum of 500 new private sessions can be started per minute per LogMeIn Rescue account. Time calculation uses a rolling time method ("DateTimeNow" minus 60 seconds).

When the maximum number of concurrent sessions has been reached and a new private session is initiated for the concerned LogMeIn Rescue account, the customer is redirected to the following URL:

https://secure.logmeinrescue.com/errorpages/concurrentsessionslimitreached.aspx

Please note that the LogMeIn Rescue Technician Console has been tested with a maximum of 10,000 concurrent sessions in the queue. With more sessions in the queue, Technician Console performance may be compromised.

For information concerning the maximum number of simultaneous active private sessions, see How many customers can I support simultaneously?

In case of channel sessions:

There is no restriction on the number of concurrent channel sessions.

Please note that the LogMeIn Rescue Technician Console has been tested with a maximum of 10,000 concurrent sessions in the queue. With more sessions in the queue, Technician Console performance may be compromised.