Glamorgan had a 114-run first-innings deficit but they reached 303 for six in their second dig, largely thanks to Stewart Walters' stately 98 and Mark Wallace's 61no.
Hostilities will begin in the morning with the Welsh side 189 ahead.
Division leaders Northamptonshire ended day three in front of Leicestershire by 215 runs despite being reduced to 94 for five.
Australian seamer Trent Copeland's superb figures of seven for 63 were key to bowling out the Foxes for 234, while Ollie Freckingham took his match haul to nine wickets with three for 28 when Northamptonshire took the crease.
Leicestershire's Shiv Thakor, with 64no, and Northants' James Middlebrook, with 43, were alone in getting to grips with conditions.
Meanwhile, fourteen wickets fell on the first day between Kent and Worcestershire at Canterbury.
The Pears opted to bowl first and promptly dismissed the hosts for 159, evergreen seamer Alan Richardson returning five for 41.
Sam Northeast managed 52 at the top of the order, while Moeen Ali (54) also reached a half-century as Worcestershire closed on a relatively positive 105 for four.
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