In Microsoft Outlook 2016 for Mac or Outlook for Mac 2011, you cannot propose a new time when you respond to a meeting request.
This feature is not available in Outlook for Mac 2011 and in Outlook 2016 for Mac versions 15.8.2 and earlier.
The Propose New Time feature is available in Outlook 2016 for Mac version 15.9 and later versions when you are connected to Microsoft Exchange Server 2013 SP1 or a later version. To obtain version 15.9 of Outlook 2016 for Mac, apply the April 14, 2015, update for Outlook for Mac for Office 365. To do this, see the following Microsoft Knowledge Base article:
3055707 MS15-033: Description of the update for Microsoft Outlook for Mac for Office 365: April 14, 2015
To use this feature, view a meeting request, click the Propose New Time button, and then select either Tentative and Propose New Time or Decline and Propose New Time.
Note If you are running Outlook 2016 for Mac version 15.9 or a later version and you are connected to a version of Exchange Server that is earlier than Exchange 2013 Service Pack 1 (SP1), the Propose New Time button does not appear on meeting requests.
This workaround applies if either of the following conditions is true:
You are running Outlook for Mac 2011 or Outlook 2016 for Mac version 15.8.2 or an earlier version.
You are running Outlook 2016 for Mac version 15.9 or a later version and you are connected to a version of Exchange Server that's earlier than Exchange 2013 SP1.
To work around this issue, select either Tentative or Decline in the meeting request, and then click Respond with Comments. In the body of the response, add text that advises the meeting organizer of the time that you propose for the meeting, and then send the response.
The meeting organizer will receive this response, and they can then modify the meeting and send you an updated meeting request.
For more information about accepting a new time proposal in Outlook for Mac, see the following Microsoft Knowledge Base article:
2935220 You cannot accept new meeting time proposals in Outlook for Mac