Is it possible to subset and assign in the same command? For example, I would like to reduce an assay to 1000 features for illustrative purposes. But, it causes an error.

melanomaData[, , 2] <- melanomaData[1:1000, , 2]
Error in .nextMethod(value = value, x = x) : 
  'value' must be a ExperimentList object (or coercible to a ExperimentList object)

What's the correct way to subset one assay and reassign it to the same variable?

I believe you need the [[ accessor for that.

> library(MulitAssayExperiment)
> data(miniACC)
> miniACC
A MultiAssayExperiment object of 5 listed
 experiments with user-defined names and respective classes.
 Containing an ExperimentList class object of length 5:
 [1] RNASeq2GeneNorm: SummarizedExperiment with 198 rows and 79 columns
 [2] gistict: SummarizedExperiment with 198 rows and 90 columns
 [3] RPPAArray: SummarizedExperiment with 33 rows and 46 columns
 [4] Mutations: matrix with 97 rows and 90 columns
 [5] miRNASeqGene: SummarizedExperiment with 471 rows and 80 columns
Functionality:
 experiments() - obtain the ExperimentList instance
 colData() - the primary/phenotype DataFrame
 sampleMap() - the sample coordination DataFrame
 `$`, `[`, `[[` - extract colData columns, subset, or experiment
 *Format() - convert into a long or wide DataFrame
 assays() - convert ExperimentList to a SimpleList of matrices
 exportClass() - save data to flat files

> miniACC[[2]] <-  miniACC[[2]][1:10,]
> miniACC
A MultiAssayExperiment object of 5 listed
 experiments with user-defined names and respective classes.
 Containing an ExperimentList class object of length 5:
 [1] RNASeq2GeneNorm: SummarizedExperiment with 198 rows and 79 columns
 [2] gistict: SummarizedExperiment with 10 rows and 90 columns
 [3] RPPAArray: SummarizedExperiment with 33 rows and 46 columns
 [4] Mutations: matrix with 97 rows and 90 columns
 [5] miRNASeqGene: SummarizedExperiment with 471 rows and 80 columns
Functionality:
 experiments() - obtain the ExperimentList instance
 colData() - the primary/phenotype DataFrame
 sampleMap() - the sample coordination DataFrame
 `$`, `[`, `[[` - extract colData columns, subset, or experiment
 *Format() - convert into a long or wide DataFrame
 assays() - convert ExperimentList to a SimpleList of matrices
 exportClass() - save data to flat files

Any other iteration appears to generate an invalid object, if it works at all.