Ok, I found a way around this in the "Core" theme.
1) I made a copy of the "Profile.template.php" file and put it in my theme.
2) I opened the file in my editor and did a search for the class "profileview".
3) At the first "profileview" (line 53), I copied and duplicated that line right below it and added a tab to the new second one (duplicated copy on line 54).
4) Then I changed "profileview" to "profileview1" on line 54 (shown below).
// Display the basic information about the user
echo '
<div id="profileview" class="flow_auto">
<div id="profileview1" class="flow_auto">
<div class="cat_bar">
<h3 class="catbg">
5) Then I went down to line 960 (will be 961 after the edit in #3) and changed the "profileview" there to "profileview2" and saved the file.
6) Now went to open the "index.css" file of the *core* theme (in the theme I'm working on of course) and went down to line ~2579.
7)
/* Fixes for the core theme */
#profileview
{
padding: 1px;
border: 1px solid #696969;
background-color: #ecedf3;
}
#profileview .content
{
border: none;
}
#basicinfo .content
{
padding: 1em;
}
#detailedinfo .content
{
padding: 0.7em 1.2em;
border-left: 1px solid #aaa;
}
/* Fixes for the core theme */
#profileview
{
padding: 1px;
border: 1px solid #696969;
background-color: #ecedf3;
}
#profileview .content
{
border: none;
}
#profileview1
{
border: 1px solid #696969;
background-color: #ecedf3;
}
#profileview2
{
padding: 1px;
border: 1px solid #696969;
background-color: #ecedf3;
}
#profileview2 .content
{
border: none;
}
#basicinfo .content
{
padding: 1em;
background-color: #ecedf3;
}
#detailedinfo .content
{
padding: 0.7em 1.2em;
border-left: 1px solid #aaa;
}
And you're done. Adjust the background colors to your pleasing.

Marking this as solved.
