I have posted a similar question before but it was poorly formulated so I'll try to make it better this time.

I have 258 samples and they are all settled in 26 different clusters, with some clusters with only 1 sample and some with over 40. The clusters are mutually exclusive. I will illustrate it with an example due to the large number of clusters and samples.

Let's say I have 12 samples in 4 blocks

> cluster <- as.factor(rep(c("A","B","C","D"), each = 3))
> design<-model.matrix(~cluster)

The design matrix will look like

> design
   (Intercept) clusterB clusterC clusterD
1            1        0        0        0
2            1        0        0        0
3            1        0        0        0
4            1        1        0        0
5            1        1        0        0
6            1        1        0        0
7            1        0        1        0
8            1        0        1        0
9            1        0        1        0
10           1        0        0        1
11           1        0        0        1
12           1        0        0        1
attr(,"assign")
[1] 0 1 1 1
attr(,"contrasts")
attr(,"contrasts")$cluster
[1] "contr.treatment"

If I want to compare A with B+C+D, do I just do this?

> makeContrasts("Intercept-(clusterB+clusterC+clusterD)/3",levels = design)
           Contrasts
Levels      Intercept-(clusterB+clusterC+clusterD)/3
  Intercept                                1.0000000
  clusterB                                -0.3333333
  clusterC                                -0.3333333
  clusterD                                -0.3333333

And for B vs A+C+D, do I just do this?

> makeContrasts("clusterB-(Intercept+clusterC+clusterD)/3",levels = design)
           Contrasts
Levels      clusterB-(Intercept+clusterC+clusterD)/3
  Intercept                               -0.3333333
  clusterB                                 1.0000000
  clusterC                                -0.3333333
  clusterD                                -0.3333333

I need to use the intercept because mod0 argument in svaseq(), if not taking the intercept as the null model, won't work, but this make it kind of complicated for myself.

No, that's not how you do things.

First, about your terminology. In general, 'blocks' sounds like some sort of batch-effect like thing that one would normally want to account for, but that is uninteresting. If you mean 'groups' or 'treatments' or 'phenotypes' or some interesting thing that one might care to know something about, then you should call them what they are. If these are blocks of samples that were processed separately, or for which you expect there to be technical differences, then it's rather uncommon for people to be testing for differences (you usually control for those differences, rather than test for them). Aaaanyway,

If you have an intercept, and you are using the default treatment contrasts (which is what you are doing here), then the intercept is a 'baseline' group (in your case clusterA), and all the other coefficients are estimates of the difference between a given cluster and the baseline. So clusterB is actually clusterB - clusterA, and inherently is a contrast.

So it makes no sense to do what you are doing. For example, your first contrast is actually clusterA - (clusterB - clusterA + clusterC - clusterA + clusterD - clusterA)/3, which is definitely something, but probably not what you intend.

You are correct that svaseq needs a model with an intercept, but that has nothing to do with anything but running svaseq. The requirement for an intercept doesn't extend to the modeling step. So you can run svaseq with an intercept, and then add those surrogate variables to your design matrix, and then use a design matrix without an intercept to make any comparison you desire using makeContrasts.