Upvote:4
Time spent under a residence permit does not count towards the short-stay limit so in principle it should be possible to get another 90 days when it expires (see Does tourist visa (90 days) apply after a long-term visa ends in Schengen countries?).
In any case, leaving and reentering the Schengen area or going back home would not in itself open any right to stay longer. Unlike other countries, the Schengen area has no notion of βresetting the clockβ, being admitted for a new period of stay or anything like that. Getting a regular short-stay visa is not an option either. If you have exhausted your 90 days, the only solutions to stay longer is waiting the cooling off period out or getting a national visa/permit like your current Swedish residence permit.
But see also Staying in Europe (Schengen and non-Schengen) for one year.