A little late to the punch, but this question appeared high on the Google results.
If you right-click on a group in the Grouping Window, and choose Group Properties, it opens a Group Properties window. In that window you can add additional fields to group by. You can then add static columns for those fields into the Tablix.
In the RDLC file, this looks like:
<TablixRowHierarchy>
<TablixMembers>
<TablixMember>
<Group Name="Level_Block_Name">
<GroupExpressions>
<GroupExpression>=Fields!Level.Value</GroupExpression>
<GroupExpression>=Fields!Block.Value</GroupExpression>
<GroupExpression>=Fields!Name.Value</GroupExpression>
</GroupExpressions>
</Group>
<SortExpressions>
<SortExpression>
<Value>=Fields!Level.Value</Value>
</SortExpression>
<SortExpression>
<Value>=Fields!Block.Value</Value>
</SortExpression>
<SortExpression>
<Value>=Fields!Name.Value</Value>
</SortExpression>
</SortExpressions>
...