Recent progress in cosmology has relied on combining different cosmological probes. In an earlier work, we implemented an integrated approach to cosmology where the probes are combined into a common framework at the map level. This has the advantage of taking full account of the correlations between the different probes, to provide a stringent test of systematics and of the validity of the cosmological model. We extend this analysis to include not only cosmic microwave background (CMB) temperature, galaxy clustering, and weak lensing from the Sloan Digital Sky Survey (SDSS) but also CMB lensing, weak lensing from Dark Energy Survey Science Verification (DES SV) data, type Ia supernova, and H0 measurements. This yields 12 auto- and cross-power spectra which include the CMB temperature power spectrum, cosmic shear, galaxy clustering, galaxy-galaxy lensing, CMB lensing cross-correlation along with other cross-correlations, as well as background probes. Furthermore, we extend the treatment of systematic uncertainties by studying the impact of intrinsic alignments, baryonic corrections, residual foregrounds in the CMB temperature, and calibration factors for the different power spectra. For ΛCDM, we find results that are consistent with our earlier work. Given our enlarged data set and systematics treatment, this confirms the robustness of our analysis and results. Furthermore, we find that our best-fit cosmological model gives a good fit to all the data we consider with no signs of tensions within our analysis. We also find our constraints to be consistent with those found by the joint analysis of the WMAP9, SPT, and ACT CMB experiments and the KiDS weak lensing survey. Comparing with the Planck Collaboration results, we see a broad agreement, but there are indications of a tension from the marginalized constraints in most pairs of cosmological parameters. Since our analysis includes CMB temperature Planck data at 10< <610, the tension appears to arise between the Planck high- modes and the other measurements. Furthermore, we find the constraints on the probe calibration parameters to be in agreement with expectations, showing that the data sets are mutually consistent. In particular, this yields a confirmation of the amplitude calibration of the weak lensing measurements from the SDSS, DES SV, and Planck CMB lensing from our integrated analysis.