Firstly, remember all the limitations of uncontrolled trials (see e.g. ICH E10 Choice of Control Group in clinical trials). So, let's assume they have some value in your case (the good thing is that to some extent good statistical methods will discount such trials a lot, if some assumptions are not meet).
Secondly, one of the more obvious approaches is to use a generalized linear mixed effects model (GLMM). The very simplest form would be
$$g(E Y_{ij}) = \beta_i + \gamma_j + \delta_{ij},$$
where $Y_{ij}$ is the outcome in arm $j$ of trial $i$, $g()$ is the link function, $\beta_i$ is the main effect for trial $i$, $\gamma_j$ is the (fixed) main effect for treatment $j$ and $\delta_{ij}$ is the deviation from effect off treatment $j$ in trial $i$ (treatment by trial interaction). Crucially, $\beta_i$ and $\delta_{ij}$ are random effects (which makes this model identifiable) that e.g. follow $N(0, \tau_\beta)$ and $N(0, \tau_\delta)$ distributions. If you do a frequentist analysis this does not matter, but I believe one would usually use a sum to zero constraint on the treatment main effects for a Bayesian analysis.
This type of model can be implemented in most statistical packages, e.g. the author of the article I mention provides SAS code. Since you are effectively doing an arm-based network meta analysis, looking at the software used by the practioners in that field might be useful. Stan (can be used in R via the rstan package) could be another very flexible choice that gives you complete freedom of specification for both a Bayesian and frequentist analysis.
