Rice joins from Southern Division One South side Willand Rovers.
The 22-year-old joined Rovers in 2020.
Formerly on the books at Plymouth Argyle, Yeovil Town and Barnstaple Town, he-joined Bideford AFC for a second spell from Taunton Town in December 2019.
Knowles, 28, signs from league rivals Salisbury.
He had joined the Whites from Southern Division One South side Frome Town in June 2019.
He had been with the Somerset outfit since February 2018 after arriving from then-league rivals Tiverton Town.
An attacking midfielder with excellent technical ability, Knowles was originally part of the Exeter City youth set-up.
His other previous other clubs include Evesham United and Paulton Rovers and he also had a loan stint with Weston-super-Mare.
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