In general, only one floating or full screen insert can be triggered at a given time. For instance, if an In-App Message insert and a Coupon insert are both configured with the same trigger, and the user falls into the active audience for both, only one of the inserts will be displayed. The insert that is shown depends on capping, latest insert update, and other parameters.
Inserts which replace elements in the app, such as the Modify Text insert, and inserts which are contextual to a screen's elements, such as the Mobile Tooltip, can co-exist on the same screen. Banner inserts can also co-exist with other inserts on the same screen.
In order to alert you to potential clashes, you will see a warning in the Insert Console if you define two inserts with the same audience and triggers. It is important to note though that because audience calculation is dynamic, Insert cannot detect all potential clashes at the time of insert creation.