Health risks from galactic cosmic rays (GCR) in space travel above low earth orbit remain a concern. For many years accelerator experiments investigating space radiation induced prevalence of murine Harderian gland (HG) tumorigenesis have been performed to help estimate GCR risks. Most studies used acute, relatively low fluence, exposures. Results on a broad spectrum of individual ions and linear energy transfers (LETs) have become available. However, in space, the crew are exposed simultaneously to many different GCR. Recent upgrades at the Brookhaven NASA Space Radiation Laboratory (NSRL) now allow mixtures in the form of different one-ion beams delivered in rapid sequence. This paper uses the results of three two-ion mixture experiments to illustrate conceptual, mathematical, computational, and statistical aspects of synergy analyses and also acts as an interim report on the mixture experiments' results. The results were interpreted using the following: (a) accumulated data from HG one-ion accelerator experiments; (b) incremental effect additivity synergy theory rather than simple effect additivity synergy theory; (c) parsimonious models for one-ion dose-effect relations; and (d), computer-implemented numerical methods encapsulated in freely available open source customized software. The main conclusions are the following. As yet, the murine HG tumorigenesis experimental studies show synergy in only one case out of three. Moreover, some theoretical arguments suggest GCR-simulating mixed beams are not likely to be synergistic. However, more studies relevant to possible synergy are needed by various groups that are studying various endpoints. Especially important is the possibility of synergy among high-LET radiations, since individual high-LET ions have large relative biological effectiveness for many endpoints. Selected terminology, symbols, and abbreviations. DER - dose-effect relation; E(d) - DER of a one-ion beam, where d is dose; HG prevalence p - in this paper, p is the number of mice with at least one Harderian gland tumor divided by the number of mice that are at risk of developing Harderian gland tumors (so that in this paper prevalence p can never, conceptually speaking, be greater than 1); IEA - incremental effect additivity synergy theory; synergy level - a specification, exemplified in Fig. 5, of how clear-cut an observed synergy is; mixmix principle - a consistency condition on a synergy theory which insures that the synergy theory treats mixtures of agent mixtures in a mathematically self-consistent way; NTE - non-targeted effect(s); NSNA - neither synergy nor antagonism; SEA - simple effect additivity synergy theory; TE - targeted effect(s); β* - ion speed relative to the speed of light, with 0 < β* < 1; SLI - swift light ion(s).