combining parts

[James E. Bailey]

Is it possible to combine four parts into two voices on one staff,  
ideally with one voice stems up and the other voice stems down? I've  
gotten as far as two voices combined into one voice with stems in the  
direction I want, but every time I add the other voice, I either lose  
the two voice configuration, or I lose the stem settings. For  
reference, I've been playing with the following as my example.
ErsteStimme = { c''8 b' b' a' g' g' f' e' }
ZweiteStimme = { a'8 a' g' f' f' e' d' c' }
DritteStimme = { e'8 f' c' d' e' e' b a }
VierteStimme = { c'8 d' a b c' b g f }
OneAB = {
        <<
                \set Staff.printPartCombineTexts = ##f
                \partcombine
                <<\stemUp \ErsteStimme>>
                <<\stemUp \ZweiteStimme>>
        >>
}
TwoAB = {
        <<
                \set Staff.printPartCombineTexts = ##f
                \partcombine
                <<\stemDown \DritteStimme>>
                <<\stemDown \VierteStimme>>
        >>
}
\score {
        \new Staff {
                <<
                        <<\stemUp \OneAB>>
                        <<\stemDown \TwoAB>>
                >>
        }
}

I also tried <<\new Voice = "1" \with {\remove Rest_engraver} {\OneAB}  
\new Voice = "2" \with {\remove Rest_engraver} {\TwoAB}>>, and  
<<{\OneAB}\\{\TwoAB}>>, and various things involving \stemUp and  
\stemDown, and I just can't seem to get it work.