ANOVA RCB design; multiple items in groups

Good day!

I have a study that seems to fit the criteria for an ANOVA using a randomized complete block design. The research is on the effect of one drug on a blood parameter, but we assume that another measurable factor also affects the blood parameter (hence our blocking).

Yet, we cannot design the experiment to have one study subject in each treatment-block combination. Because the blocking factor is determined through another blood test that is run parallel to the investigated blood parameter. This means that we will end up with study subjects that are not equally divided between the treatment-block combinations. Is this allowed? All the examples I read of ANOVA RCB designs have only one study subject in each of the treatment-block combinations.

Is our problem better suited to regression model?

Many thanks!