Defending champions Warwickshire were bowled out for 158 on day two at Taunton but Somerset declined to enforce the follow-on despite earning a first-innings advantage of 248.
Somerset instead reached 46-1 in their second innings to extend their lead to 294 at stumps. Marcus Trescothick (37) fell lbw to Jeetan Patel's off-spin for the second time in the match shortly before the close.
Warwickshire's batsmen had earlier struggled in windy conditions with Rikki Clarke's 37-ball 31 the top score of an innings lasting 65.4 overs.
Alfonso Thomas led the Somerset attack with 3-29 and there were two wickets each for seamer Jamie Overton (2-47) and left-arm spinner Jack Leach (2-43).
Jim Troughton (26), Laurie Evans (25) and Chris Woakes (21) all wasted starts, while Clarke's promising contribution was ended by a direct hit from Marcus Trescothick that saw him run out.
At the start of the day, Somerset advanced their first innings from 358-6 to 406 all out.
Jos Buttler, on 90 overnight, completed his third first-class century and finished 119 not out.
Medium pacer Clarke took the final three wickets to finish with figures of 4-70.