Overweight and obese dogs can develop metabolic dysfunction, characterized by an inflammatory response and involvement of liver functions. If a modulation of the gut microbiome and its interaction with the gut–liver axis is implicated in the development of metabolic dysfunction, exploration becomes necessary. Over the past decade, diverse therapeutic approaches have emerged to target pathogenic factors involved in metabolic dysfunction. This study investigated the impact of a supplement with hepatoprotective activity, containing extracts of Silybum marianum, prebiotics, probiotics, n-3 polyunsaturated fatty acids, vitamins, and minerals on hematological markers of liver functions and inflammation, as well as on the intestinal microbiota of 10 overweight adult dogs over a 35-day time span. Animals underwent clinical and laboratory evaluations every 7 days, both before the administration of the supplement (T0) and after 7, 14, 21, 28, and 35 days (T1, T2, T3, T4, and T5). In comparison to T0, a significant (p < 0.05) decrease in ALP, glucose, direct bilirubin, and CRP was observed from T3 to T5. The alpha diversity of the fecal microbiota significantly decreased (p < 0.05) only at T1, with high variability observed between dogs. Total short-chain fatty acid and lactic acid were also lower at T1 (p < 0.05) compared to the other times of sampling. The beta diversity of the fecal microbiota failed to show a clear pattern in relation to the sampling times. These results of blood parameters in overweight dogs show a reduction of the inflammation and an improvement of metabolic status during the study period, but the effective contribution of the supplement in this clinical outcome deserves further investigation. Furthermore, the considerable individual variability observed in the microbiome hinders the confident detection of supplement effects.