In MS Access, if you right-click on a linked table and select Design, Access will tell you that you cannot make design changes to a linked table. Although it's true that you can't do it from the UI, you can do it using VBA. . .In fact, this approach will work even if the back-end file is an older format such as Access 97 or 2000.

These examples use the DAO object library, so we need a reference to it; Also, we qualify the Dim's just in case there is also a ref to the ADO library.

In the following example, the linked table is Table1 and we want to add a long integer field named NewLongField. Note that 1) use the actual table name, not an alias (if there is one) and 2) you need exclusive access to the back-end file.

Dim db As DAO.Database
Dim fld As DAO.Field
Dim tdf As DAO.TableDef
Const MDB = "C:\My Documents\MyDatabase.mdb"
Set db = OpenDatabase(MDB)
Set tdf = db.TableDefs("Table1")
With tdf
  Set fld = .CreateField("NewLongField", dbLong)
  .Fields.Append fld
  Set fld = Nothing
End With
Set tdf = Nothing
db.Close
Set db = Nothing

...when adding a date field, the "Set fld = " line will look like this:
Set fld = .CreateField("NewDateField", dbDate)

...a text field will also require the size, like this:
Set fld = .CreateField("NewTextField", dbText, 50)

..boolean fields can be added like this:
Set fld = .CreateField("NewBooleanField", dbBoolean)
however this will display as -1 (True) or 0 (False). If you want to have the customary checkbox display, here is the complete code for that:

Dim db As DAO.Database
Dim fld As DAO.Field
Dim prp As DAO.Property
Dim tdf As DAO.TableDef
Const MDB = "C:\My Documents\MyDatabase.mdb"
Set db = OpenDatabase(MDB)
Set tdf = db.TableDefs("Table1")
With tdf
  Set fld = .CreateField("NewBooleanField", dbBoolean)
  fld.DefaultValue = 0
  .Fields.Append fld
  Set prp = .CreateProperty("DisplayControl", dbInteger, acCheckBox)
  fld.Properties.Append prp
  Set prp = .CreateProperty("Format", dbText, "Yes/No")
  fld.Properties.Append prp
  Set prp = Nothing
  Set fld = Nothing
End With
Set tdf = Nothing
db.Close
Set db = Nothing