How do I unlock the other Alpha slots in my troop formation?

Each troop formation that you unlock will have an Evolution (research) tree associated with it. Look for them in the Evolution Fungi (research center). The first one is called March Troop I.

The first slot for an alpha in the troop march is opened with the first item in the research tree. Primary Leadership.

Then the second one is opened about half way down. Secondary Leadership.

The final one is the last item in the tree. Tertiary Leadership.

You need to do this for all of the 4 marches that you will eventually unlock.

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