Bolivia was part of the Viceroyalty of the River Plate, and representatives from Bolivia's southern provinces were part of the congress that declared Argentine independence in 1816. Both countries were, up to that point, the same country.
The civil war in Argentina is what really prevented Argentina stretching up to Lake Titicaca.
If Argentine forces were properly founded when San Martin disembarked in Peru, they could have launched a land offensive through Bolivia, which would have shortened the war and made Bolivia just cluster of Argentine provinces.
If the Argentine 'national' government wasn't wary of the other Argentine provinces when Sucre defeated the royalists IOTL and negotiated with Bolivar keeping Bolivia as an integral part of Argentina, Bolivar would have agreed.
So either way can work.
Uruguay is harder, since Argentina would need a decisive victory against Portugal/Brazil and its much larger navy to keep it.
Paraguay is probably out of the cards. There is no way the Paraguayans would accept it, and it would require Argentina going to war against Paraguay on her own, while still watching over Brazil, and it would be so costly I don't think any Argentine government think it's in their best interest to keep the fighting going.