To address the logistical part of the question, the Wikivoyage page on Ciudad del Este, Paraguay notes the following:
The most common way to arrive is across the Puente de la Amistad (Friendship Bridge) which connects Ciudad del Este in Paraguay and Foz do Iguaçu in Brazil. There are frequent bus connections, also to and from Puerto Iguazú in Argentina. Taxis sometimes do the trans-border trip as well.
A couple of km south of Ciudad del Este, where Rio Paraná and Rio Iguaçu join, is a ferry crossing to Puerto Iguazú in Argentina without crossing Brazilian territory. The ferry runs hourly during daylight hours for AR$5. There's a bus to Ciudad del Este passing close-by. From the centre (Av. General Bernardino Caballero), take a bus labeled Tres Fronteras (destination, not the company name) and ask to be dropped at la balsa (the ferry). Both countries have immigration facilities on their respective side of the river, so the ferry can be used not only for day tours but also for official border crossings.
It therefore appears that it is possible to cross the Brazil–Argentina border and the Brazil–Paraguay border via road, and that the ferry can be used to cross the Argentina–Paraguay border. So a loop is in principle possible, assuming that you have the appropriate travel documents for all three countries.