I think the only way to do this is to transform it into a single band and color that in the normal way. Fortunately, GeoServer provides a way to do this using Rendering Transformations and Jiffle.
Something like (untested):
<Transformation>
<ogc:Function name="ras:Jiffle">
<ogc:Function name="parameter">
<ogc:Literal>coverage</ogc:Literal>
</ogc:Function>
<ogc:Function name="parameter">
<ogc:Literal>script</ogc:Literal>
<ogc:Literal>
b1 = src[1];
b2 = src[2];
dest = (b1*2)+b2;
</ogc:Literal>
</ogc:Function>
</ogc:Function>
</Transformation>
<Rule>
<RasterSymbolizer>
<Opacity>1.0</Opacity>
<ColorMap type="values">
<ColorMapEntry color="#000000" quantity="0"/>
<ColorMapEntry color="#ff0000" quantity="1"/>
<ColorMapEntry color="#ffff00" quantity="2"/>
<ColorMapEntry color="#ffffff" quantity="3"/>
</ColorMap>
</RasterSymbolizer>
</Rule>
Note: the use of values
in the color map to color only pixels that match that value.