I have 10 different DTD's and one specific part of the DTD repeats in all of the DTD's. I want to store this repeating DTD as another separate DTD and use it as a reference in all the other DTD's.

Yes, this is possible using External Parameter Entities. Here's the sample logon.dtd

<!ELEMENT USERID (#PCDATA)>
<!ELEMENT PASSWORD (#PCDATA)>

Here's another DTD which references the logon.dtd

<!ELEMENT NAME (#PCDATA)>
<!ELEMENT AGE (#PCDATA)>
<!ENTITY % logon SYSTEM "logon.dtd">
%logon;