Save grayscale multipage TIFF without affecting intensity values

I feel like this has a very simple solution but I can't find it! I load some TIFF stacks of the same size, estimate the mean stack (mean slice 1 / mean slice 2 / ...) and then try to save the new mean stack. The input images are 32-bit with values, say, between 0.8-1.5. When I save the mean image I get an 8-bit TIFF stack with mostly white pixels; I think all values above 1 are converted to 255 and the rest scaled accordingly.

How can I save a 32-bit TIFF stack that preserves the 0.8-1.5 intensity range and doesn't do any intensity scaling? I assume this is possible because I used ImageJ to get the mean of two stacks and works absolutely fine. Thanks.