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A Toplevel class can be constructed using object-oriented programming without any side-effects by following the principles of encapsulation, abstraction, and immutability. This means that the class should be designed to minimize the effects it has on the rest of the system and reduce the potential for conflicts or errors.

The following steps can be taken to ensure that a Toplevel class is constructed without side-effects:

1. Use private and protected access modifiers to limit the visibility of the class's properties and methods.

2. Use immutable data structures to ensure that the class's properties cannot be modified after they are initialized.

3. Design the class to be easily testable, with clear and concise unit tests that verify its functionality.

4. Avoid global state and side-effects in the class's methods, such as modifying external files or databases.

5. Use dependency injection to pass in any dependencies the class requires, rather than allowing the class to create them itself.

By following these principles, a Toplevel class can be constructed using object-oriented programming without introducing any side-effects into the system. This helps ensure that the class is reliable, maintainable, and does not interfere with other parts of the program.