Somerfield (2021a, b, c) published a series of related articles explaining how ANOSIM can be applied to a variety of designs.  I reprint some of their key tables here.

Designs are provided for:

• Crossed or nested designs
• Ordered or unordered factors.  For example, high / medium / low would be ordered whereas prairie / forest / wetland would be unordered.
• Replication at the lowest level of the design

These tables were prepared for and focus on ANOSIM, but elements such as how permutations need to be restricted for each term are also relevant for statistical techniques such as PERMANOVA and RRPP.  Also included (right-hand column) are some ecological examples that illustrate possible usages of each design.

Additional information about how to analyze complex designs is provided by Anderson & ter Braak (2003) – see in particular Tables AI through AIV in their Appendix.

1-Factor and 2-Factor Designs

Table 1 from Somerfield et al. (2021b) provides the following guidance for using ANOSIM to analyze 1-factor (options 1a to 1d) and 2-factor (options 2a to 2n) experimental designs using the generalized ANOSIM test statistic.

The table is in two parts as it spans two pages in the original publication.

3-Factor Designs

Somerfield et al. (2021c) provides the following guidance for using ANOSIM to analyze 3-factor (options 3a to 3m) experimental designs using the generalized ANOSIM test statistic.

The table is in two parts as it spans two pages in the original publication.

References

Somerfield, P.J., K.R. Clarke, and R.N. Gorley. 2021a. A generalized analysis of similarities (ANOSIM) statistic for designs with ordered factors. Austral Ecology 46:901-910.

Somerfield, P.J., K.R. Clarke, and R.N. Gorley. 2021b. Analysis of similarities (ANOSIM) for 2-way layouts using a generalized ANOSIM statistic, with comparative notes on Permutational Multivariate Analysis of Variance (PERMANOVA). Austral Ecology 46:911-926.

Somerfield, P.J., K.R. Clarke, and R.N. Gorley. 2021c. Analysis of similarities (ANOSIM) for 3-way designs. Austral Ecology 46:927-941.