Somerset are still 226 runs from saving the follow-on at Headingley after Yorkshire made more in-roads on a rain-shortened third day.
Rain stopped play just before lunch with Somerset sitting on 190-5 in response to Yorkshire's 505-9 declared after Tim Bresnan, who is pushing for a place in the England squad ahead of the first Test against New Zealand at Lord's next week, claimed two early wickets and leg-spinner Adil Rashid captured two in two balls.
The visitors could have been much worse off had Yorkshire had not also spilled two catches, although they did get an early breakthrough when England opener Nick Compton offered no stroke to the second ball of the day from Bresnan and was out lbw.
Nightwatchman Jack Leach survived a confident shout for a catch behind the wicket off Jack Brooks but after edging Bresnan through the slips for four he had his off-stump flattened by the same bowler.
Bresnan's double strike left Somerset on 123-3 but Alviro Peterson and James Hildreth stopped the slide with some confident shots, although the South Africa batsman would have gone for 24 if his edge off Steve Patterson had been held low down at second slip by Adam Lyth.
Bresnan was replaced by Richard Pyrah, who was hit to the mid-wicket boundary by Hildreth, but the batsman then had an escape as Joe Sayers fluffed a chance at third slip.
Unperturbed, Hildreth stroked the next ball through the covers for four to take him to 10,000 runs in first class cricket.
Rashid found himself unemployed until he was finally given a bowl at 169-3 in the 62nd over but Peterson went on to cut him for four to complete his half-century from 76 balls with seven boundaries.
There was revenge for the leg-spinner in his next over when he beat Peterson through the air and he drove a catch to Patterson at mid-on. Arul Suppiah came to the crease and promptly left it, caught by Sayers at short leg off his first ball.
Rashid had to wait until his following over to attempt the hat-trick but Jos Buttler survived and the rain came shortly afterwards.