Oh yeah, there are lots of things you can do. It looks like you wanna stay with the C being in the bass, so here are some chords you can add:
C / D-E-G-C (or other inversions) Cadd9
/ D-G-B (or other inversions G/C
/ C-F-A (or other inversions) F/C
C / Bb-D-F-A BbM7/C
/ Bb-D-E-A or Bb-D-E-G C13
/ A-C-E-G Am7/C
/ Ab-C-D-G, F# Dm7b5/C
C / F-Bb-D or F-A-Bb-D Bb/C
/ E-Bb-D or E-A-Bb-D C9 or C13
/ F-G-A-C Fadd9/C
/ D-F-Ab-C Dm7b5/C
*switch to C minor
C / Ab-C-Eb-G or Ab-C-Eb (or other inversions) AbM7/C or Ab/C
/ Bb-D-F (or other inversions) Bb/C
/ Ab-Bb-C-Eb Abadd9/C
/ F-Bb-Eb Bbsus4/C
/ F-Bb-D Bb/C
/ C, D
/ G-C-E *switch back to major