Can we insert multiple dropdown within another multiple dropdown.

Short answer: no.

I'm not quite sure what you even want - but I'm guessing you're after something that we'd usually do via what we call "cascading dropdowns".  What exactly is your use case / requirement?  You haven't provided much detail here for us to go on..

a!sideBySideItem(
                          item: a!multipleDropdownField_20r2(
                            label: "Therapeutic Area",
                            labelPosition: "ABOVE",
                            placeholder: "---Select all that Apply---",
                            choiceLabels: index(local!therapeuticArea.data, "name", {}),
                            choiceValues: index(
                              local!therapeuticArea.data,
                              "therapeuticAreaId",
                              {}
                            ),
                            value: if(
                              rule!APN_isBlank(ri!therapeuticAreaIds),
                              null,
                              ri!therapeuticAreaIds
                            ),
                            saveInto: {
                              ri!therapeuticAreaIds,
                              a!save(ri!primaryProductIds, null),
                              a!save(ri!studyRequest.otherProduct, null)
                            },
                            required: true,
                            disabled: and(
                              ri!studyRequest.externalStudyStatus <> cons!ISR_TEXT_STATUS_APP_PI_DRAFT,
                              not(
                                rule!APN_isBlank(ri!studyRequest.externalStudyStatus)
                              )
                            ),
                            validations: {}
                          )
                        ),

In the above code if we select any one value from the "index(local!therapeuticArea.data,"name",{})" .For example if we choose "cat" from the choice values then again another multifield dropdown values should visible when we choose on the "cat" in the same multidropdown field.

let me know is there any solution for it

Hello sireesha,

I have not come across such requirement. But my guess is you cannot since you will have to filter data based on your first selection as you are using a multiple dropdown. And when you are filtering the data, you will not be able to filter array values for a single data set. Hence your scenario is not possible. 

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.

sireesha said:

if we choose "cat" from the choice values then again another multifield dropdown values should visible when we choose on the "cat" in the same multidropdown field.

I strongly recommend against this approach - it would be nearly impossible to manage, and also not a good user experience in almost any case I can think of.  Instead, you should consider having a heuristic conditionality set in a local variable to detect when "cat" is selected in the initial dropdown, and when it is, show an additional dropdown consisting of the additional selections you want the user to be able to choose from.