The US Centers for Disease Control has a page which discusses simultaneous administration of SHINGRIX with other vaccines:
CDC general recommendations advise that recombinant and adjuvanted vaccines, such as Shingrix, can be administered concomitantly, at different anatomic sites, with other adult vaccines, including COVID-19 vaccines. Concomitant administration of Shingrix with Fluarix Quadrivalent (influenza vaccine, QIV), 23-valent pneumococcal polysaccharide vaccine (Pneumovax23, PPSV23) and Tetanus Toxoid, Reduced Diphtheria Toxoid and Acellular Pertussis Vaccine, Adsorbed (Boostrix) has been studied, and there was no evidence for interference in the immune response to either vaccine or safety concerns. Coadministration of Shingrix with adjuvanted influenza vaccine (Fluad) and COVID-19 vaccines is being studied. [Emphasis added]
Since both Twinrix and Arexvy are adult recommended recombinant and adjuvanted vaccines, we can conclude that general recommendations advise they can be administered at the same time, but at different sites.
However, from the CDC page, we can also surmise that no studies are available specifically for Twinrix or Arexvy. The information provided by GSK (the manufacturer of both vaccines) says as much:
The package insert for Twinrix notes:
There are no data to assess the concomitant use of TWINRIX with other vaccines
Meanwhile, the package insert for Arexvy notes:
Concomitant administration of AREXVY with other vaccines are unknown.
Thus, the CDC generally recommends that all recombinant and adjuvanted vaccines can be administered together. There is no information to suggest and increased risk of adverse events, but there have been no specific studies to detect them other than the Vaccine Adverse Event Reporting System.