Can we insert multiple dropdown within another multiple dropdown.

Because you have not conveyed a lot of your use case the question you were raising, maybe the question was kind of misleading. 
Of course, you cannot display drop-down components in another drop down component. 

If the use case is about to show a specific selection of other drop-down components based on the selection in the first drop-down component.
This is possible in Appian. You just trigger this with the showWhen parameter in the drop-down components which will show up accordingly to the selection of the names in the major (first) drop down component. 

I hope this makes sense.

Because you have not conveyed a lot of your use case the question you were raising, maybe the question was kind of misleading. 
Of course, you cannot display drop-down components in another drop down component. 

If the use case is about to show a specific selection of other drop-down components based on the selection in the first drop-down component.
This is possible in Appian. You just trigger this with the showWhen parameter in the drop-down components which will show up accordingly to the selection of the names in the major (first) drop down component. 

I hope this makes sense.