Arlington National Cemetery officials recently discovered eight instances in which family members were buried at the same grave site but all the names were not added to the headstones marking the graves.

The cemetery’s management also estimated the cost of accounting for every one of the cemetery’s 330,000 graves — a task that they acknowledge may never be completed — to be $4.3 million.

The disclosure of the problems with the headstones came in an update Wednesday from Army Secretary John McHugh to Sen. Claire McCaskill (D-Mo.), who demanded a status report on the cemetery two weeks ago. It comes of the eve of a hearing by a House subcommittee that is expected to grill Army leaders about accountability at the cemetery.

In June, an Army inspector general’s report found widespread problems, including unmarked and mismarked graves, and urns that had been dug up and dumped in a landfill.

Since then, officials have discovered additional problems, including a single grave that held eight sets of cremated remains, three of which cannot be identified and will be reburied as “unknown.” The existence of that mass grave is the focus of a criminal probe.

As they try to figure out who is buried where, officials have said they would continue to find problems. In addition to the previously reported problems, the new issues include the following:

l Grounds crews twice replaced an existing headstone that correctly identified the deceased with a headstone that was for someone else — meaning two sets of remains were unidentified and two others were wrongly identified.

l A person who was buried one spot over from his or her headstone.

l Three additional cases of graves without headstones.

l A niche cover that had not been taken down in the columbarium after the person’s remains had been transferred to another cemetery.

Cemetery officials would not release the names of the people involved and would say only that the incidents occurred before the cemetery’s new management took over last year.

They said the incidents were discovered by family members or cemetery workers who alerted the new management that they knew where problems existed.

Army officials have attempted to contact the affected families but have not been able to in every case because families had not provided up-to-date contact information.

In his letter to McCaskill, McHugh said he is confident that the cemetery’s new leadership team is “working tirelessly to correct the difficulties that we have had at Arlington National Cemetery in the past.”

He said that since the inspector general’s report found problems in three of the cemetery’s 70 sections, officials have examined more than 22,000 grave sites and have found additional problems.

In eight cases, they found that family members’ names had not been added to headstones. At Arlington, families are often buried in a single grave and share a headstone. If a spouse dies after the service member, for example, his or her name is supposed to be added to the back of the headstone.

Even since the new management took over at Arlington, there have been problems with burials. In one case, an admiral whose family had requested that he be buried near the USS Forrestal Memorial was mistakenly buried in another spot. The cemetery knew where he was buried at all times, and the mistake was quickly discovered and fixed, Kathryn Condon, head of the Army’s National Cemeteries Program, said in a recent interview.

Condon also said grounds crews mistakenly swapped the sites of two other people buried at roughly the same time. She said the mistake was caused by human error and fixed the same day.