This blog has colorized nested blockquotes now.
test
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For the colorizing, I used the following CSS code in a plug-in that lets you enter custom CSS. I tried to use a child WordPress theme but was having trouble getting that working.
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blockquote blockquote blockquote blockquote blockquote { 
    background: #FFA500;
 
} 
blockquote blockquote blockquote blockquote { 
    background: #FFC0CB;
 
} 
blockquote blockquote blockquote { 
    background: #ADD8E6;
 
} 
blockquote blockquote { 
    background: #98FB98;
 
} 
blockquote { 
    background: #FFF6DB;
 
    font-size: 100%;
 
} 
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Without setting the font-size to 100%, the blockquotes were larger than my regular text, and I did not want that.
The font-size being set to 100% seems to cascade down to the nested blockquotes, though, so I only had to set it for the first one.