Have you tried somethig like this?
.showme{display: none;}
.showhim:hover .showme{display : block;}
.hideme{display:block;}
.showhim:hover .hideme{display:none;}
<div class="showhim">HOVER ME
<div class="showme">hai</div>
<div class="hideme">bye</div>
</div>
I dont know any reason why it shouldn't be possible.