The present version of iStudio Publisher doesn't support layers, apart from the separate layers provided by the master pages and a body pages. However, on either a body page or a master page you do have complete control over the front to back ordering (layering) of different shapes.
Newly drawn shapes are always positioned in front (on top) of existing shapes.
If you click on a pile of shapes to select one, the frontmost shape will always be selected. This can make it difficult to select an underlying shape that is completely covered by other shapes. To select an underlying shape, select any shape on the page and then press the Tab key repeatedly to cycle the current shape selection through all of the shapes on the page. If you click and hold down the left mouse button while doing this, once the required shape has been selected you can adjust its position using the mouse.
You can adjust the front to back 'z' order of a pile of shapes from the Arrange menu or via the corresponding toolbar icons. Having selected an underlying shape you wish to work on, a useful technique is to choose menu option Arrange > Bring to Front, after which the shape can be selected with the mouse.
The Arrange menu includes four different commands for changing the front to back 'z’ order. Bring to Front and Send to Back work as you might expect, moving the current shape selection to the top or bottom of a pile of shapes. The other two commands, Bring Forward and Send Backward, enable adjustment of the intermediate position within a pile of shapes, which can be useful if you want to stack them in a particular order.