You will need to read the column value first and then add new values then update.
Get Multi-valued People Picker Field Value (if Allow multiple selections enabled!) using PowerShell:
Add-PSSnapin Microsoft.SharePoint.PowerShell -ErrorAction SilentlyContinue
#Configuration Variables
$SiteURL = "<replace site url>"
$ListName = "Tasks"
$FieldName="Assigned To"
#Get site and List objects
$web = Get-SPWeb $SiteURL
$list= $web.lists[$listName]
#Iterate through each row in the list
foreach ($Item in $list.Items)
{
if($item[$FieldName])
{
#Get People picker field values collection
$UserCollection = New-Object Microsoft.Sharepoint.SPFieldUserValueCollection($Web,$item[$FieldName].ToString())
Write-host Item ID: $item["ID"]
#Get each User from the Person or Group field
foreach($User in $UserCollection)
{
#Get the Display Name of the user
Write-host $User.LookupValue
#Get the Login Name (Account ID)
Write-host $User.User
#Get the E-mail
Write-host $User.User.Email
}
}
}
Update Multiple Values People Picker Field using PowerShell script
Add-PSSnapin Microsoft.SharePoint.PowerShell -ErrorAction SilentlyContinue
#Configuration Variables
$SiteURL = "http://portal.crescent.com/sites/Sales"
$ListName = "Tasks"
$FieldName="Assigned To"
#Get site and List objects
$web = Get-SPWeb $SiteURL
$list= $web.lists[$listName]
#Get the List Item to update
$ListItem = $List.GetItemByID(2)
#User Account to set
$UserAccounts="Crescent\Salaudeen; Crescent\Ravi"
$UserAccountsColl = $UserAccounts -split ';'
$UserCollection = new-object Microsoft.SharePoint.SPFieldUserValueCollection
foreach($UserAccount in $UserAccountsColl)
{
#Get the User
$User=$web.EnsureUser($UserAccount)
#Add to collection
$UserFieldValue = new-object Microsoft.SharePoint.SPFieldUserValue($Web, $User.ID, $User.LoginName)
$UserCollection.Add($UserFieldValue)
}
#update the Multiple value Person or Group field
$ListItem[$FieldName] = $UserCollection
$ListItem.Update()
Source: http://www.sharepointdiary.com/2015/12/get-set-person-or-group-people-picker-field-values-using-powershell.html