Adding to Multi-Value Lookup Column via PowerShell (SP 2013)

Is there any way via PowerShell to add data to a multi-value Lookup column instead of overwriting it?

For example, the item already has stuff checked off in the Lookup column. Values 1 and 2 are already checked. But I want to add 3 without overwriting 1 and 2.

Here is a snip of my code:

foreach($row in $csvVariable)
{
$updateitem = $list.GetItems($query) | Where {$_["Entity Name"] -eq $row.AccountIdName}

$lookupfield = $list.Fields["Lookup"] -as [Microsoft.SharePoint.SPFieldLookup];
$lookuplist = $webDestination.Lists[[Guid]$lookupfield.LookupList]; 
$sourcefield =  $lookupfield.LookupField;            
$lookupitem = $lookuplist.Items | Where {$_["Title"] -eq $row.new_UpperTierIdName}
$lookupvalue = New-Object Microsoft.SharePoint.SPFieldLookupValue($lookupitem.ID,$lookupitem.ID.ToString());  

$updateitem["Lookup Column"] = $lookupvalue
$updateitem.Update()
}

The csv file is a many-to-many report that changes every day. I just want to be able to add values to the lookup column, not clear and re-set.