I think that multiple encumberments can be placed on a property at once. I think that if a property has multiple issues with it then it can definitely be placed with multiple encumberments. I also think that it would be a difficult thing for the owner of such a property to take care of.
Not only are multiple encumbents, or liens, allowed in the American legal system, there are specific rules in place to determine what happens in that instance. Generally, liens receive priority based on when they are filed with the appropriate county, with the exception of mortgage liens. Liens that have priority are always paid off first.
There are tons of liens that can be place on property to fulfill a debt. If you own one piece of property as your only legal asset, there can be liens placed upon it for when the property is sold within a certain timeframe. These liens include mechanic's liens, tax liens and liens for personal loans.
Yes, multiple encumberments can be placed on a property at once, because there can be more than one person who has a claim to the property. For example, a person can take out multiple mortgages. Another person can have a claim to drive a vehicle across the property to access their own property.