I suspect a collection/dictionary approach may be more useful:
Option Explicit
Private oDays As Object

Public Sub AddDate(Value As Date)
    Dim sDate As String
    sDate = CStr(Value)
    If oDays.Exists(sDate) Then
        oDays(sDate) = oDays(sDate) + 1
    Else
        oDays.Add sDate, 1
    End If
End Sub

Public Property Get DatesWorked() As Object
    Set DatesWorked = oDays
End Property


Private Sub Class_Initialize()
    Set oDays = CreateObject("Scripting.Dictionary")
End Sub
Sub test()
    Dim oEngineers As Collection
    Dim oEngineer As cEngineer
    Dim vDatesWorked
    Dim vDays
    Dim x As Long
    
    Set oEngineers = New Collection
    
    For x = 1 To 10
        Set oEngineer = New cEngineer
        oEngineers.Add oEngineer, "Kyle" & x
    Next x
    
    oEngineers("Kyle1").AddDate #5/1/2013#
    oEngineers("Kyle1").AddDate #5/2/2013#
    oEngineers("Kyle1").AddDate #5/1/2013#
    oEngineers("Kyle1").AddDate #5/4/2013#
    
    vDatesWorked = oEngineers("Kyle1").DatesWorked.Keys
    vDays = oEngineers("Kyle1").DatesWorked.Items
End Sub