Future space travel to the earth's moon or the planet Mars will likely lead to the selection of experienced International Space Station (ISS) or lunar crew persons for subsequent lunar or mars missions. Major concerns for space travel are galactic cosmic ray (GCR) risks of cancer and circulatory diseases. However large uncertainties in risk prediction occur due to the quantitative and qualitative differences in heavy ion microscopic energy deposition leading to differences in biological effects compared to low LET radiation. In addition, there are sparse radiobiology data and absence of epidemiology data for heavy ions and other high LET radiation. Non-targeted effects (NTEs) are found in radiobiology studies to increase the biological effectiveness of high LET radiation at low dose for cancer related endpoints. In this paper the most recent version of the NASA Space Cancer Risk model (NSCR-2022) is used to predict mission risks while considering NTEs in solid cancer risk predictions. I discuss predictions of space radiation risks of cancer and circulatory disease mortality for US Whites and US Asian-Pacific Islander (API) populations for 6-month ISS, 80-day lunar missions, and combined ISS-lunar mission. Model predictions suggest NTE increase cancer risks by about ∼2.3 fold over a model that ignores NTEs. US API are predicted to have a lower cancer risks of about 30% compared to US Whites. Cancer risks are slightly less than additive for multiple missions, which is due to the decease of risk with age of exposure and the increased competition with background risks as radiation risks increase. The inclusion of circulatory risks increases mortality estimates about 25% and 37% for females and males, respectively in the model ignoring NTEs, and 20% and 30% when NTEs are assumed to modify solid cancer risk. The predictions made here for combined ISS and lunar missions suggest risks are within risk limit recommendations by the National Council on Radiation Protection and Measurements (NCRP) for such missions.