Is it possible to sort lookup columns that allow multiple values or is there any alternative that can be applied in a modern list view?
I don’t think there is any OOB solution to sort lookup column in modern list view.
You need to consider custom solutions with SPFx extension.
In SP 2010 & 2013 it's not possible to sort by multi-value lookup columns, I don't know about Sharepoint Online. But presumably it's not possible.
In your lookup column, if you go to Edit Column there is a section titled
Add a column to show each of these additional fields: - you can select additional columns to bring to your destination list. It might be worth experimenting with these to see if an 'additional column' can be filtered.