Three members of the family - Bandhuprakash Pal, his wife Beauty and their eight year old son Angan - were found murdered in their home at Jiaganj on Tuesday.
The victims were apparently hacked to death and their bodies lay in a pool of blood.
"We have detained two more persons on Saturday. Two others were detained earlier. Another two were released after questioning," a senior police officer said.
The BJP and the Rashtriya Swayamsevak Sangh (RSS) have claimed that Bandhuprakash had been attending RSS' weekly programme Milan over the past few months.
The police have, however, ruled out any political angle in the case and claimed that the victims' family members denied Bandhuprakash was affiliated to any political group.
The police have also claimed that Bandhuprakash was in a serious financial crisis and said they found a diary note suggesting serious differences in the family.
"Prima facie it seems to be a case of personal enmity and it has nothing to do with politics," the police said in a twitter post on Friday.
The state police Criminal Investigation Department has now become part of the investigation.
Famed filmmaker Aparna Sen described the incident as "shame" for the people of the state and asked the Chief Minister Mamata Banerjee to ensure the perpetrators were brought to justice.
The incident has also triggered slugfest between state governor Jagdeep Dhankhar and the ruling Trinamool Congress.
While the governor on Thursday condemned the incident as dastardly and barbaric, the ruling Trinamool gave a strong counter alleging that Dhankhar was 'transgressing his constitutional jurisdiction'.
The governor in his strong statement had said the incident has "shocked the conscience" on account of its enormity and it was "reflective of intolerance and worrisome law and order situation".