Can I have a field in which the user is given the option of selecting from a dropdown list or entering their own custom address?

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You can do this with field scripting.  Please see instructions below:
 
You would create three fields on the master PDF.  You would set them up as follows:
1)  Custom - The placement of this field on the master pdf is irrelevant.  This should be a text field coming from user entry.  On the Data Capture tab, set the user control type to be a Text Area.  On the format tab, set the field usage to hide the field.
2)  DropDown - The placement of this field on the master pdf is irrelevant.  This should be a text field coming from user entry.  On the Data Capture tab, set the user control type to be a Dropdown List.  Set up your locations/addresses in the dropdown list.  On the format tab, set the field usage to hide the field.
3)  Address - This should be placed on the master pdf in the exact location in which you would like the address to appear.  This should be a text field coming from Field scripting.  On the format tab, set the field usage for proof and production.  On the field scripting tab, you would choose to use a VB script.  You would enter the following script:
Ifs(Custom="", Dropdown, Custom)
 
This means that if the Custom field is blank or empty, then use the contents of the Dropdown field, otherwise use the contents of the Custom field.  Please see this link to test a sample template set up in this fashion.  You will notice in the sample that we have used an entry block to group the address options and provide further instructions.
 
Note: Do not copy and paste the VB script sample directly from your web browser into eDocBuilder, as the formatting used to display it in your browser may also be copied and may make your script work incorrectly. Please first paste the script into a plain text editor (such as Notepad). Then copy the script from the plain text editor and paste it into the Field Scripting tab of your field in eDocBuilder.