under the current rules, it goes like this.
Chain 1: pay 500 for Offering, normal summon a monster
Chain 2: pay 500 for Offering, normal summon a monster
Chain 3: pay 500 for Offering , normal summon a monster
so Offering will chain to its own effect (however this is only possible if the trap is already face up on the field). so monsters that are normal summoned in chain 2 and 3 cannot be trap-holed or bottomless or torrential.
of course, theres nothing stopping you from using it one at a time and not chaining, just saying that the above use is also legal under the current rules.
http://yugioh-wiki.net/index.php?cmd=read&page=%A1%D4%B7%EC%A4%CE%C2%E5%BD%FE%A1%D5&word=%B7%EC%A4%CE%C2%E5%BD%FE