I believe your only hope is to apply for a national "D" visa from the country where the summer school is located. Mention in your application that you aren't eligible to attend on a C visa because of the 90/180 rule.
The problem may be that the program may be unable to sponsor its students for a national D student visa, whether because of the brief nature of the program or for some other reason. If that is true, you may be out of luck. There may be an administrator at the summer program who can tell you whether this is the case.
If your current program is in the same country where the summer program is located, there is a chance that you may be able to extend your stay. To do this, you would apply to the office responsible for issuing residence permits in that country. Thanks to MertKarakaya for mentioning this in a comment.