How to change sponsor of Social Visa

You can apply for a 60 day visit visa without having a sponsor.  That visa can also be extended here up to 4 times, each time good for an additional 30 days.  This visa is essentially the same as a sosbud visa. 

At some point during the extension periods you will likely be asked to provide a sponsor.  If you don't have one, you can hire a local visa agent or in some cases, a travel agent to act as you sponsor (for a fee of course).

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Agreed, good post.

An Italian citizen should have little trouble (save the usual paperwork),  especially as you intend to move around the country, making any possible suspicion of illegal working unlikely to be considered.

Just for information, why do you wish to visit this wonderful country?

Many thanks for replying.
Well, although we've been travelling around a bit, we've never been to Asia before. Indonesia is pretty big and far as well, and it has so many different places to visit indeed. Would just like to extend our stay the more we can, since we have some time off and staying for just a short period would not really make sense. And, we think it is not that likely that italians come over to find a job, but we could be wrong. This is not the case at all though.
We read about the 6-month-visit visa without the sponsor but we could not figure out whether it was still possible to apply for it or not. Local embassy didn't provide us with clear information.
We will dig more into this, thanks!