Attaching the screenshot in the answer

I'm not sure i understand you well...

I'd prefer to use Linq To Xml[^].

//define search criteria
string searchterm = "private";
StringComparison comparison = StringComparison.InvariantCulture;

//create instance of XDocument
XDocument xdoc = Xdocument.Load("FullFileName");

//define parent node  for ObjectType nodes
var otsparent = xdoc.Descendants("Types").SingleOrDefault();

//find ObjectType nodes Name starts with "private"
var ots2copy = xdoc.Descendants("ObjectType")
    .Where(x=>x.Attribute("Name").Value.StartsWith(searchterm, comparison))
    .ToList();

//loop through the list of nodes which meet criteria
int i = 1;
foreach(XElement original in ots2copy)
{
    //create deep copy of original node
    XElement copy = new XElement(original);
    //change Name attribute
    copy.Attribute("Name").Value += i.ToString();
    //add a copy to parent node
    otsparent.Add(copy);
    i++;
}

//...

//Save document at the end of process
//xdoc.Save("NewFullFileName.xml");

Result:

<Types>
  <ObjectType Name="private.C53da99cf09a845c6ad14b0412d101132" DisplayName="Graphic" Description="Graphic" Icon="TGML.gif" Base="tgml.TGML" Abstract="0" Implements="" DefaultProperty="" Version="1"></ObjectType>
  <ObjectType Name="private.C99cf176f956241a6aabb850d8ff8e44f" DisplayName="Function Block Program" Description="Function block program" Icon="Menta.gif" Base="menta.Program" Abstract="0" Implements="" DefaultProperty="" Version="1">
    <Verbs>
      <Verb Type="Contain" Name="menta.Module" minOccurs="0" maxOccurs="2147483647" ContainType="DerivedAndBase" SubTarget="Config" />
      <Verb Type="Contain" Name="menta.Alarm" minOccurs="0" maxOccurs="2147483647" ContainType="DerivedAndBase" SubTarget="Config" />
      <Verb Type="Contain" Name="system.schedulecommon.ScheduleBase" minOccurs="0" maxOccurs="2147483647" ContainType="DerivedAndBase" SubTarget="Config" />
    </Verbs>
  </ObjectType>
  <ObjectType Name="private.C53da99cf09a845c6ad14b0412d1011321" DisplayName="Graphic" Description="Graphic" Icon="TGML.gif" Base="tgml.TGML" Abstract="0" Implements="" DefaultProperty="" Version="1"></ObjectType>
  <ObjectType Name="private.C99cf176f956241a6aabb850d8ff8e44f2" DisplayName="Function Block Program" Description="Function block program" Icon="Menta.gif" Base="menta.Program" Abstract="0" Implements="" DefaultProperty="" Version="1">
    <Verbs>
      <Verb Type="Contain" Name="menta.Module" minOccurs="0" maxOccurs="2147483647" ContainType="DerivedAndBase" SubTarget="Config" />
      <Verb Type="Contain" Name="menta.Alarm" minOccurs="0" maxOccurs="2147483647" ContainType="DerivedAndBase" SubTarget="Config" />
      <Verb Type="Contain" Name="system.schedulecommon.ScheduleBase" minOccurs="0" maxOccurs="2147483647" ContainType="DerivedAndBase" SubTarget="Config" />
    </Verbs>
  </ObjectType>
</Types>

On the same manner, you have to copy OI nodes. At this moment it isn't clear what nodes have to be copied.

For further details, please see:
LINQ to XML Overview (C#)[^]
.NET Language-Integrated Query for XML Data[^]
Basic Queries (LINQ to XML) (C#)[^]

Another way to achieve that is to use XmlDocument class[^], which provides a way to to load, validate, edit, add (even a clone[^] node), and position XML in a document.

Try! Good luck!

[EDIT]
To copy OI nodes:

var oisparent = xdoc.Descendants("ExportedObjects").SingleOrDefault();
var ois2copy = xdoc.Descendants("OI")
    .Where(x=>x.Descendants("OI").Count()>1)
    .Select((x, i)=> new
        {
            index = i,
            ois = x
        })
    .ToList();

int j = 1;
foreach(var indexednodes in ois2copy)
{
    //create deep copy of original node
    XElement copy = new XElement(indexednodes.ois);
    foreach(XElement oi in copy.Descendants("OI").Where(x=>x.Attribute("TYPE").Value.StartsWith(searchterm, comparison)))
    {
        //change Name attribute
        oi.Attribute("TYPE").Value += j.ToString();
    }
    //add a copy to parent node
    oisparent.Add(copy);
    j++;
}