OK Here's my idea of how the A part might be completed plus an invented B part wich uses the same resolutions as the A part and then a C part which uses the idea that leeneia suggested, starting in the relative major key.
X:1 T:unknown L:1/8 M:3/4 K:Em E3F GA | Be e4 | e3 f ed | B4 AB | cB AB cA | BA G2 B,2 | CE A2 G2 | F6 | E3 F GA | Be e4 | e3 f ed | B4 AB | cB AB cA | BA GA BG | B,G F3 E | E6 |] e2 B3 G | c2 F4 | B3 A GF | GF GA B2 | cB cB Ac | BA G2 B,2 | CE A2G2 | F6 | e2 B3 G | c2 F4 | B3 A GF | GF GA B2 | ed cB Ac | BA GA BG | B,G F3 E | E6 |] G3 A Bc | dB AB G2 | e3 d ce | d6 | c3 B Ac | BA G2 B,2 | CE A2 G2 | F6 | E3 F GA | BG A2 B2 | c3 d ef | g4 fe | dg fe dB | ce dc BG | A3 G FD | E6 :|] W: W:Bars one to eight are the original fragment. W:Bars nine to sixteen are a guess at the second half of the A part. W:Bars seventeen to thirtytwo are an invented B part using the resolutions from part A W:W:Bars thirtythree to fortyeight following leeneia's suggestion to start in Relative Major key.