$DemoUser = 'Domain\username'
$DemoPass = 'complexpassword'
$Command = "ECHO 'Hello world'; WhoAmi;"
$StdOutLogFile = "$env:windir\temp\PowerShellElevatedStdOut.log"

$SecurePassword = ConvertTo-SecureString $DemoPass -AsPlainText -Force
$Credential = New-Object System.Management.Automation.PSCredential $DemoUser, $securePassword

"Running '$Command' as current user"
Start-Process Powershell.exe -NoNewWindow -ArgumentList "-Command $Command" -RedirectStandardOutput $StdOutLogFile -Wait
Get-Content -Path $StdOutLogFile  #Retrieve the output from the external process

"Running '$Command' as $DemoUser"
Start-Process Powershell.exe -NoNewWindow -ArgumentList "-Command $Command" -RedirectStandardOutput $StdOutLogFile -Wait -Credential $Credential -WorkingDirectory 'C:\Windows\System32'
Get-Content -Path $StdOutLogFile #Retrieve the output from the external process