You're right, there's no support for negative delays, you'll have to work the other way.
In Inspector -> Animate, click the Build Order button at the bottom. In the pop-up window you'll see a list of the objects on the page that have an action attached to them, and you can adjust the timing from here.
For the first object, it may be set to start automatically, or on click, as you prefer.
For the second object, you can set it to start 'With Build 1', and add a delay.
So, for example, if the first object has a 10-second animation and you want the second object to start half way through, you'll add a 5-second delay to the second object. Object 2's timer starts at the same time as Object 1 (because you have it set 'With Build 1'), but it's delayed by 5 seconds.

So you will have to do the math, but it should give you the effect you want.