This is not new as projects only sell a fraction of their tokens as IEO, the remaining tokens are usually sold as ICO. Major part of the tokens are usually sold in private sales.
For Private Sale, that is usually done often at the beginning before entering the other sales stages. The question @OP is doing ICO and IEO together. Because doing it together will make people confused and the funds will be divided during the sale. Therefore it is better determined before selling, It is better to do in IEO or ICO.
But there are some icos were doing it. I remember i were seeing an ico was still running its ICO and at the same time that ico has tried to get the fund from the exchange site too. It looks like that kind of ico used exchange site as a formality to make its token will be more easier to be listed on the exchange site.
Even the fund will be divided but it will go to the same person or project.