George Santos and Iain Ward are the latest additions to the treatment table with groin strains, with Paul Raven also out of action after pulling his thigh after five minutes of the Mariners 2-0 deafeat against Watford at Vicarage Road on Saturday.
It is unclear how long the trio will be sidelined with the manager hoping to know more by Tuesday.
Groves himself has suffered a setback with his calf strain, while skipper John McDermott has damaged the same area of his calf that ruled him out for four months last term.
With Steve Chettle visiting a specialist on Monday about his suspect back, Groves' concerns are completed by Alan Pouton's calf strain.
"We are hoping that Pouts, Wardy and George are short term and that they should be okay for Saturday," said the Town manager.
"At the moment we just don't know and it's too early to say. We'll have to see how they settle down and we should have a clearer picture tomorrow.
"I've had a setback with my calf and, because you're constantly putting weight on it, it's a difficult area.
"Macca is one we're having to be very careful with. His injury is in the same spot where he ruptured it last season. We're being very cautious with him."
Meanwhile, Groves has rubbished reports in certain Sunday newspapers that he had offered to resign after the 3-0 home defeat by Reading: "I don't know where they got that from. You shouldn't believe everything you read in the papers!
"There's no truth in it at all. I'll fight on."