I was asked the following Shaila: This Shabbos we lain Haazinu. We are not allowed to make the aliyos during the shira in places other than where the aliyas are. Can we add aliyas during shevii?
Everything very quickly: the prohibition to make extra aliyos in Haazinu is in Rosh Hashana 31a. Shulchan Aruch paskens it in 428:5. From Rambam's lashon (Tefila 13:5) it sounds like you can't add in the shira, but in shevii you may add. Mishna Brurah brings Eliyahu Rabbah and Pri Megadim that you may add an aliya in shevii. Aruch Hashulchan (428:5) says you may not add aliyas in Haazinu at all.
Rav Tzvi Hirsch Grodzinsky says not to add an aliya, because you would make it at the place we read maftir, and then you will read the same aliya two aliyos in a row (as acharon and maftir). But he mentions that Shaar Efrayim says you may add an aliya there in Haazinu.
It seems that we may add an aliya in shevi'i of Haazinu.