Update: The answer is "Aye". Gyre down to see more than one case and an rh negative changing into an rh positive and vice versa.

This is one claim that has been made a lot. And until recently I have never received additional information to any of the claims I have heard.
Then of course there are cases of chimerism where you have dissimilar blood types in your veins. And 1 test tin show one blood blazon, another examination the other.
In that location is nevertheless one story out there which documents Demi-Lee Brennan and the one in 6 Billion possibility of a transplant changing your claret type.

The 15-yr-old liver transplant patient is the first person in the world to take on the immune organisation and claret blazon of her donor, negating the demand to take anti-rejection drugs for the rest of her life. The phenomenon, which has been documented in the New England Periodical of Medicine, has amazed doctors, who say they have no idea how information technology occurred.

She had the liver transplant done and and so:

Ix months subsequently, when her condition worsened and she was readmitted, doctors were shocked to find that her blood type had changed. The head of hematology, Julie Curtin, said she was stunned when she realised Demi-Lee was now O-positive, rather than O-negative.

"I was convinced we had fabricated a fault, so we tested information technology again and it came upward the same. And so we tested her parents and they were both O-negative, so it was confirmed that Demi absolutely had to have been O-negative."

You can read more of the story hither:

Transplant girl's blood change a 'miracle'

But as I have stated before, reading a mainstream newspaper commodity is one thing (the interpretation of sometimes not sufficiently educated journalists tin can potentially bring the wrong conclusions) … finding the actual study is another matter:

Acute fulminant hepatitis subsequently a nonspecific viral illness adult in a previously well ix-yr-old girl. Her claret grouping was O, RhD-negative. She was referred to our establishment, and at the time of admission she had markedly elevated aminotransferase levels and evidence of marked synthetic dysfunction. Extensive testing ruled out known viral, metabolic, drug-related, and autoimmune causes, and a diagnosis of "not–A-to-G viral hepatitis" was made. A liver biopsy was not performed because of severe underlying coagulopathy.

Given the patient's fulminant hepatic failure requiring mechanical ventilation, urgent liver transplantation was performed with the use of a whole-organ transplant from an O, RhD-positive 12-year-old male person donor who was positive for cytomegalovirus (CMV) (the recipient was also CMV-positive) and who died of hypoxic brain injury. The whole liver was transplanted (cold ischemic fourth dimension, 9 hours 46 minutes), and the biliary anastomosis was a choledochocholedochostomy. The HLA status of the donor was A34,68;B50,76;DR4,13, and the recipient'south HLA status was A2,24;B37,62;DR7,9.

Nine months afterward transplantation, a small-bowel obstruction developed, requiring surgical segmentation of adhesions and resection of an ileal ring. Routine preoperative claret grouping revealed that the patient's blood grouping had inverse from O, RhD-negative, to O, RhD-positive (the donor'southward blood group), and a weakly positive direct antiglobulin test indicated blanket of ruddy blood cells with IgG antibodies. At that time, there was no evidence of spherocytosis on the blood film to suggest hemolysis; the hemoglobin level was 95 yard per liter. This finding was confirmed by the Australian Carmine Cross Blood Service. Both parents had group O, RhD-negative blood with the phenotype ccdee, whereas their girl'south phenotype was now cDEe. Withal, serum samples showed mixed-field reactions with anti-D and anti-E typing.

Source and more:

How a liver transplant has changed a young girl's rh factor

Then this was an rh negative person irresolute into an rh positive. Can information technology exist the other way effectually? Yep.
See this:

We study a female person patient whose Rh phenotype shifted from RhD-positive to RhD-negative over a 3-twelvemonth period (1991–94), during which time she was treated with mastectomy (1992) and local irradiation for a low-grade recurrent breast cancer. She was diagnosed with chronic myeloid leukaemia in 1994, and has since then received chemotherapy. The patient was repeatedly typed as O, RhD-positive betwixt 1965 and 1991 and was repeatedly institute RhD-negative later on 1994. Bcr-Abl transcripts typical of Ph1 chromosome were detected. Molecular assay indicated that the patient was heterozygous at the RH locus, carrying one haplotype in which the RHD gene exhibited a single nucleotide deletion (G600) resulting in a frameshift and premature terminate codon, and a normal RHCE cistron (allele Ce). The second haplotype contained only the RHCE gene (allele ce) and was normal. Further analysis carried out on full leucocytes, purified neutrophils, EBV-lymphoblastoid cell line and cultured erythroblasts indicated that the G600 deletion was restricted to the myeloid lineage. No modification of other blood grouping antigens could be detected. These findings propose a somatic mutation which most probably occurred in a stalk prison cell common to the myeloid lineage.

Source:
Shift from Rh-positive to Rh-negative phenotype caused by a somatic mutation within the RHD gene in a patient with chronic myelocytic leukaemia