The purpose of this study is to evaluate the safety, tolerability, and efficacy of AntiBKV in reducing BKV DNAemia and progression to biopsy-confirmed BKVAN in kidney transplant recipients. This study has an operationally seamless phase II/III design. The phase II part will evaluate the safety of AntiBKV in kidney transplant recipients and establish antiviral proof of concept. The phase II part includes a dose-comparison part to generate additional PK and PD data of AntiBKV. The phase III part will assess the efficacy of AntiBKV in kidney transplant recipients. For both the phase II and phase III parts, participants will be randomized to receive either four doses of AntiBKV or four doses of placebo (every four weeks). In phase II, 60 participants will be first randomized (1:1) to receive either four doses of 1,000 mg of AntiBKV or placebo. In an additional dose-comparison extension, another 30 participants will be enrolled and randomized (1:1:1) to receive either four doses of 1,000 mg AntiBKV, four doses of 500 mg AntiBKV, or placebo. Based on a Day 141 analysis after phase II the sample size for the phase III part of the trial will be defined. Both the phase II and phase III parts will follow identical study assessments and schedules for participants.

Eligible participants will receive an intravenous infusion of the investigational medicinal product (IMP) that will be administered four times at a four-week interval. For the first ten participants enrolled in the study, the infusion time will be at least 60 minutes. Provided there are no safety concerns observed with the first ten participants the duration of subsequent infusions will be at least 30 minutes.

After administration of the final dose, participants will return as out participants for periodic safety, BKV DNAemia, and PK follow-up assessments until the end of the trial visits, 26 weeks post last IMP application. Regular kidney biopsies will be performed at baseline (prior to infusion) and on Day 141 (8 weeks after full dosing). An additional biopsy will be taken on Day 267 (optional) and if clinically indicated.

Inclusion Criteria:

1. Male or female aged 18 years or older
2. Kidney transplantation within 24 months prior to enrollment
3. Kidney transplant recipient with first-time BKV DNAemia (evaluated during routine clinical monitoring by the local laboratory and acknowledged by a physician within four months prior to Day 1). BKV DNAemia is either defined by BKV-DNAemia of one time >10,000 copies/mL, or >1,000 copies/mL sustained for at least one week (confirmed by two consecutive measurements. Note: The second, most recent laboratory value must be acknowledged by a physician within four months prior to Day 1)
4. Kidney transplant recipients with adequate and/or stable allograft function as indicated by estimated glomerular filtration rate ((e)GFR) ≥ 30 mL/min
5. Female subjects (if of childbearing potential) must agree to use adequate and reliable contraceptive measures throughout their participation in the trial. Contraceptive use by women should be consistent with local regulations regarding the methods of contraception for those participating in clinical studies
6. Ability to provide written informed consent

Exclusion Criteria:

1. Patients with previous diagnosis of BKV DNAemia (defined as one time > 10,000 copies/mL, or > 1,000 copies/mL sustained for at least one week (confirmed by two consecutive measurements) since last kidney transplantation
2. Known hypersensitivity to any component of the IMP
3. Transplanted kidney disease with an estimated glomerular filtration rate ((e)GFR) < 30 mL/minute at screening
4. Uncontrolled acute or chronic infection other than BKV infection at screening which might interfere with study participation at the discretion of the investigator
5. Recipients who are treated or planned to be treated with a mTOR inhibitor or belatacept as part of their immunosuppression regimen post-transplantation at the time of enrollment and during the study period
6. Recipients who are treated or planned to be treated during study participation with leflunomide at the time of enrollment and during the study period
7. Recipients who in the opinion of the investigator are likely to require antibody-depletion therapy during trial participation. Antibody-depletion therapies include but are not necessarily limited to plasmapheresis, immunoadsorption, and intravenous immunoglobulins (IVIg)
8. Recipients with active kidney transplant rejection or FSGS
9. Recipients who have medical conditions or receive concomitant medications that prevent the recipient from undergoing allograft biopsy
10. Recipients with known DSA (de novo or pre-transplantation). Kidney transplant recipients with low-level pretransplant DSAs (< 1000 mean fluorescence intensity (MFI)) can be included if no impact on the study assessments is expected by the discretion of the investigator.
11. (exclusion criterium deleted)
12. Recipients with extremely high BKV DNAemia (> 10,000,000 copies/ml) or hemorrhagic cystitis
13. Recipients who in the opinion of the investigator are likely to develop recurrent native kidney disease (e.g. IgA nephritis, FSGS, C3 glomerulonephritis)
14. Recipients with a functionally significant ureteral stricture
15. Pregnant or nursing (lactating) women
16. Known current active or latent TB or any history, in the opinion of the investigator, that confers a risk of reactivation of latent TB and precludes the use of conventional immunosuppression
17. History of splenectomy or asplenia
18. Any condition, that in the opinion of the investigator, would interfere with the evaluation of the investigational product or interpretation of the participant safety data or study results
19. History of malignancy within the past five years, except completely excised basal cell or squamous cell carcinoma of the skin, or cervical carcinoma in situ at least two years prior to screening
20. Participation in another interventional clinical trial during trial participation or within 30 days prior to the IMP dosing or planned dosing
21. History of alcoholism or drug addiction within one year of screening. Substance use disorder will be an exclusion criterion, at investigator's discretion.

Quadruple (Participant, Care Provider, Investigator, Outcomes Assessor)