The 'simple' keyboard transformation defined in Part 7 of Version 36 of the LDML specification is not compatible with the similar style long offered, for example, by Keyman. That style allows one to cycle through a set of semantically similar characters, which can be every useful if communication with the physical keyboard is unreliable, as can happen when using an X-terminal connected by wifi.
In this scheme, sequence of characters considered is not the raw sequence of characters input, but the transformation so far plus the most recently entered character. Thus one could have "T" + '\' yielding θ, "θ" and '\' yielding "ƛ", "ƛ" and '\' yielding "T", and further entries of '\' cycling round the list. In the current specification, being able to cycle indefinitely requires an infinite set of transforms.
This scheme that enables cycling is not compatible with the Microsoft implementations of dead keys. For example, in the US International keyboard, [C11][D03] yields "é", [C11][A03] yields apostrophe, and [C11][A03][D03] yields "'e". However, in the scheme supporting cycling, [C11][A03][D03] would necessarily yield "é", for [C11] is not mapped to an explicit dead key, but to the apostrophe character. Some mode selection would be required in the keyboard definition.
This posting is intended to open the discussion - much further work is required on the detail.