I agree with @Preston Botter that this is an advanced application of IRT and support the advice that you might want to look for consultation.
However, I am aware of a possible realization. The R package TAM provides a (not officially supported/documented) solution for this issue using the so-called Q-matrix (quite possible that the following idea works for other software packages as well).
First, note that in case of the 2 parameter logistic model the loading structure of the factor loadings (discrimination parameter in IRT) is estimated in order to best fit the data. More importantly, the discrimination parameter (B-matrix in TAM) is the relative weight of the respective items in the total score.
Next, the Q-matrix is typically used as a binary matrix for assigning the loading of items to different latent dimensions. However, in TAM it is possible to assign values other than zero or one to the Q-matrix. The values of Q are multiplied to the factor loadings (discrimination parameter in IRT; 1 in case of the Rasch model). Thus, we can force a loading other than 1 to items in the Rasch model (or multidimensional versions thereof).
> library(TAM)
> data(data.sim.rasch)
> data.sim <- data.sim.rasch[, 1:15]
> head(data.sim)
I1 I2 I3 I4 I5 I6 I7 I8 I9 I10 I11 I12 I13 I14 I15
[1,] 1 1 1 1 1 1 0 1 0 1 1 0 0 1 1
[2,] 0 1 0 0 0 1 1 1 0 1 1 1 1 1 0
[3,] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[4,] 1 0 1 1 0 1 1 1 0 0 1 1 1 0 0
[5,] 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1
[6,] 1 1 1 0 0 1 0 0 0 0 0 0 0 0 0
> mod1 <- TAM::tam.mml(resp = data.sim,
+ Q = data.frame("Loading" = c(rep(.5, 5), rep(1, 5), rep(2, 5))),
+ verbose = FALSE)
> mod1$item
item N M xsi.item AXsi_.Cat1 B.Cat1.Dim1
I1 I1 2000 0.8270 -1.6257163 -1.6257163 0.5
I2 I2 2000 0.8145 -1.5382826 -1.5382826 0.5
I3 I3 2000 0.8000 -1.4422434 -1.4422434 0.5
I4 I4 2000 0.7860 -1.3542285 -1.3542285 0.5
I5 I5 2000 0.7725 -1.2731382 -1.2731382 0.5
I6 I6 2000 0.7710 -1.3979913 -1.3979913 1.0
I7 I7 2000 0.7430 -1.2253834 -1.2253834 1.0
I8 I8 2000 0.7435 -1.2283610 -1.2283610 1.0
I9 I9 2000 0.7295 -1.1462542 -1.1462542 1.0
I10 I10 2000 0.6945 -0.9509658 -0.9509658 1.0
I11 I11 2000 0.6905 -1.2062157 -1.2062157 2.0
I12 I12 2000 0.6615 -1.0102233 -1.0102233 2.0
I13 I13 2000 0.6515 -0.9443237 -0.9443237 2.0
I14 I14 2000 0.6415 -0.8791659 -0.8791659 2.0
I15 I15 2000 0.6000 -0.6152801 -0.6152801 2.0
A word of caution: I'm not sure of what will happen if both, relativ loading structure via Q-matrix are given and discrimination parameter are estimated.
