sheet3を追加するパターンです。シート名はSheet4です。

[Content_Types].xml

<Override PartName="/xl/worksheets/sheet1.xml" ContentType="application/vnd.openxmlformats-officedocument.spreadsheetml.worksheet+xml"/>
<Override PartName="/xl/worksheets/sheet2.xml" ContentType="application/vnd.openxmlformats-officedocument.spreadsheetml.worksheet+xml"/>
<Override PartName="/xl/worksheets/sheet3.xml" ContentType="application/vnd.openxmlformats-officedocument.spreadsheetml.worksheet+xml"/>

docProps/app.xml

<HeadingPairs>
<vt:vector size="2" baseType="variant"><vt:variant><vt:lpstr>ワークシート</vt:lpstr></vt:variant>
<vt:variant><vt:i4>3</vt:i4></vt:variant></vt:vector>
</HeadingPairs>
<TitlesOfParts>
<vt:vector size="3" baseType="lpstr">
<vt:lpstr>Sheet2</vt:lpstr>
<vt:lpstr>Sheet3</vt:lpstr>
<vt:lpstr>Sheet4</vt:lpstr>
</vt:vector></TitlesOfParts>

3の部分をシートの数だけ増やすのがポイントです。

一部抜粋

[元のxml]
<vt:vector size="2" baseType="lpstr">
<vt:i4>2</vt:i4>
↓
<vt:vector size="3" baseType="lpstr">
<vt:i4>3</vt:i4>

xl/workbook.xml

<sheet name="Sheet2" sheetId="2" r:id="rId1"/>
<sheet name="Sheet3" sheetId="3" r:id="rId2"/>
<sheet name="Sheet4" sheetId="4" r:id="rId7"/>

xl/_rels/workbook.xml.rels

<Relationship Id="rId3" Type="http://schemas.openxmlformats.org/officeDocument/2006/relationships/theme" Target="theme/theme1.xml"/>
<Relationship Id="rId7" Type="http://schemas.openxmlformats.org/officeDocument/2006/relationships/worksheet" Target="worksheets/sheet3.xml"/>
<Relationship Id="rId2" Type="http://schemas.openxmlformats.org/officeDocument/2006/relationships/worksheet" Target="worksheets/sheet2.xml"/>
<Relationship Id="rId1" Type="http://schemas.openxmlformats.org/officeDocument/2006/relationships/worksheet" Target="worksheets/sheet1.xml"/>
<Relationship Id="rId6" Type="http://schemas.openxmlformats.org/officeDocument/2006/relationships/calcChain" Target="calcChain.xml"/>
<Relationship Id="rId5" Type="http://schemas.openxmlformats.org/officeDocument/2006/relationships/sharedStrings" Target="sharedStrings.xml"/>
<Relationship Id="rId4" Type="http://schemas.openxmlformats.org/officeDocument/2006/relationships/styles" Target="styles.xml"/>

xlsxに圧縮してご確認ください！