A visa, whether it's a "multiple use" one like you get at the embassy or a "one time use" one like you get at the airport upon your arrival in Asuncion is ONLY GOOD FOR A 90 DAY STAY. The difference being of course that with a one time visa if you want to come back you "have to buy another visa" to get into the country. If you have the mulitple use visa, you can turn around and come back again, and again, and again….using this same visa until you passport and this visa, expire.
But again, you cannot stay in country for more than 90 days legally, unless your applying for residency. And if this is the case once your residency paperwork is submitted and is being worked, you allowed to stay until residency is achieved.
Now here's a crazy thing that is so pure "Paraguayan". If you overstay the 90 day limit, then when you leave the country the immigration folks who stamp your passport will assess a fine against you, sort of an "overstay charge". It's actually not terribly much, I think the last price someone quoted was like 500,000 Gs (a little less than $100 at today's exchange rate). So, what's so crazy about this you ask? The fine is the same whether you overstay by "one day" or "one thousand days". Of course there are also ways to extend the 90 day stay by going to immigration and paying for an extension, but in another twist of Paraguayan logic, it is more expensive to do this than to just pay the fine. If it made sense, it wouldn't be Paraguay…..