Sharepoint - How to display more than three views in SharePoint 2013

SP 2013 uses clienttemplates.js to create the those views control. You can either create a JSLink or add the following script using the script Editor webpart to the page where your list view resides.

<script type="text/javascript">
ExecuteOrDelayUntilScriptLoaded(overrideSurfacePivotCount, 'clienttemplates.js');

function overrideSurfacePivotCount() {
   ClientPivotControl.prototype.SurfacedPivotCount = 4;
};
</script>

You can find more details about the ClientPivotControl and other rendering techniques in the 'clienttemplates.debug.js'

1) You can edit the page that contains each view (Site Actions > Edit Page) and then insert a Content Editor Web Part. Within this web part, you can add links to each of your views and format/style them as needed.

2) The property that controls the default value is hidden by the XsltListViewWebPart control, so unfortunately we can't modify it to be a value of >3.

Good hint about "ClientPivotControl" here, thanks!

However, inserting the above webpart script broke my CSS on list views for anonymous users so I found another workaround and thought I'd share it.

Basically, find all occurrences of variable "SurfacedPivotCount" in c:\Program Files\Common Files\microsoft shared\Web Server Extensions\15\TEMPLATE\LAYOUTS\ files and change it's values from default 2 or 3 to 6 (anything more than 3).

There will be 8 files to edit:

1. clienttemplates.js
2. clienttemplates.debug.js
3. PivotControl.js
4. PivotControl.debug.js
5. search.analyticsrecommendation.js
6. search.analyticsrecommendation.debug.js
7. SP.UI.People.js
8. SP.UI.People.debug.js

for example in SP.UI.People.debug.js in the line:

SP.UI.People.PeopleListViewPane.get_view().$Z_0.SurfacedPivotCount = 2;

change the value from 2 to 6.