Inclusion Criteria:

* Disease indication

* For dose escalation and dose optimization (Part A and Part B):

* Participants with a histologically confirmed lymphoid neoplasm (including relapsed/refractory \[R/R\] classical Hodgkin lymphoma \[cHL\], R/R peripheral T-cell lymphoma \[PTCL\], R/R systemic anaplastic large cell lymphoma \[sALCL\] , R/R mature B-cell neoplasms, and select R/R primary cutaneous lymphomas \[PCLs\]) who in the judgment of the investigator have no appropriate standard therapy available at the time of enrollment and are a candidate for SGN-35T treatment.
* Participants must have a detectable CD30 expression level (≥1%) in tumor tissue (except cHL and ALCL where CD30 is universally expressed).
* For dose expansion (Part C)

* Participants are eligible irrespective of CD30 expression on tumor tissue.
* Participants with cHL: Participants with R/R cHL who have received at least 3 prior systemic therapies (autologous stem cell transplant \[ASCT\] and the associated high dose chemotherapy prior to ASCT are considered to be 1 prior line) and meet all of the following additional criteria:

* Participants who have not received ASCT must have refused or been deemed ineligible.
* Participants must have received or been ineligible to receive an anti-PD-1 agent.
* Participants with PTCL:

* Participants with R/R PTCL (excluding R/R sALCL) who have received at least 2 prior systemic therapies or received at least 1 prior systemic therapy and there is no other available treatment that is considered appropriate by the investigator.
* Participants with R/R sALCL must have ALK status documented and must meet one of the following criteria:

* Disease recurrence or progression following at least 2 prior systemic therapies where 1 regimen included brentuximab vedotin, or
* Disease recurrence or progression following only 1 prior line of therapy which included brentuximab vedotin, cyclophosphamide, doxorubicin, and prednisone
* An Eastern Cooperative Oncology Group (ECOG) Performance Status score ≤1.
* Fluorodeoxyglucose positron emission tomography (FDG PET) avid and bidimensional measurable disease as documented by radiographic technique (spiral CT preferred) per Lugano criteria at baseline (Cheson 2014) (not applicable for subjects with PCL).

Exclusion Criteria:

* Previous exposure to CD30 targeted therapy (exception: participants with cHL, PTCL, or PCL may have received prior brentuximab vedotin but no more than 2 prior brentuximab vedotin based lines of therapy and at least 3 months should have elapsed before enrollment).
* History of another malignancy within 3 years before the first dose of study intervention, or any evidence of residual disease from a previously diagnosed malignancy. Exceptions are malignancies with a negligible risk of metastasis or death.
* Active cerebral/meningeal disease related to the underlying malignancy.
* Received previous ASCT infusion \<12 weeks prior to first SGN-35T dose.
* Participants with previous allogeneic stem cell transplant (SCT) if they meet any of the following criteria:

* \<100 days from allogeneic SCT. Participants ≥100 days from allogeneic SCT who are stable without immunosuppressive therapy for at least 12 weeks are permitted.
* Active acute or chronic graft versus host disease or receiving immunosuppressive therapy as treatment for or prophylaxis against graft versus host disease.
* Cytomegalovirus (CMV) PCR ≥500 IU/mL, OR rising DNA levels \>5-times baseline within 1 month, OR detectable CMV PCR receiving pre-emptive therapy; prior PCR positivity that was successfully treated is acceptable provided the baseline PCR result is negative prior to the first dose of study drug.
* Grade 2 or higher pulmonary disease unrelated to underlying malignancy, or history of Grade 2 or higher drug-induced interstitial lung disease (ILD) or immune checkpoint inhibitor (ICI)-related ILD.
* Clinically significant lung disease requiring systemic corticosteroid treatment within 6 months prior to enrollment or who are suspected to have such diseases via radiographic imaging and/or functional tests conducted during the screening period.