How do I use two <#if> in a component?

#elseif

Or maybe I misunderstand your question.

JillianB - Please try the code, I have made some changes to it and used elseif instead of your second if condition.

<#if coreNode.id?? && ((coreNode.id == "Instructor") || (coreNode.id == "Income") || (coreNode.id == "BlockWorksIC") || (coreNode.id == "TTSVirtual") || (coreNode.id == "Skills") || (coreNode.id == "FTF") || (coreNode.id == "BestPractices") || (coreNode.id == "Resources"))> 

<div class='VIC_community_logo'>
<a href="/t5/Instructor-Community/ct-p/Instructor" class="VICcommunityLogo" title="Virtual Instructor Community">Virtual Instructor Community</a>
<span class="tagline">Collaborating for success.</span>
</div>
<#elseif coreNode.id?? && ((coreNode.id == "BlockWorks") || (coreNode.id == "PersonalRet") || (coreNode.id == "Training") || (coreNode.id == "BusinessRet") || (coreNode.id == "BWResources"))>
<div class='VIC_community_logo'>
<a href="/t5/BlockWorks/ct-p/BlockWorks" class="BWcommunityLogo" title="BlockWorks District Advocate Community">Blockworks District Advocate Community</a>
<span class="tagline">Collaborating for success.</span>
</div>
<#else>
<div class='hrb_community_logo'>
<a href="/" class="communityLogo" title="The Community">The Community</a>
<span class="tagline">Looking at life through tax.</span>
</div>
</#if>

Let me know if this helps. Also refer to this documentation here.