Another option would be to use a lot of light cavalry units that have decent armor; i.e. prodromoi. They can catch up with those horse archers and easily beat most of them in melee.

That's more expensive though, and probably less realistic than including extra archers/slingers.

I don't know if it's realistic but when I'm dealing with steppe armies I simply don't bother to include any phalangites at all. They can absorb arrows very well, but that's about it - the infantry units that steppe factions use are generally mediocre or less, so thureophoroi are preferable because they're more mobile and versatile.