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Can a redstone latch in Minecraft Java Edition be supplemented with a toggle function?

SR latches and T-flip-flops are trivial circuitry in Minecraft redstone, but it appears that there is little to be found for a circuit that combines both, allowing for both SR and T functionality.
I envision an SR-T latch to have set, reset, and toggle inputs respectively, but all connected to the same memory cell. This means that the output can be controlled by setting it, resetting it, and toggling it all at once. Just like an SR latch, pressing S or R when the cell is already in that state should do nothing.
All of my circuitry so far has been "unclean" implementations, either a bodged wiring to add a toggle to an SR latch, or bodged wiring to add SR inputs to a T-flip-flop. What is the best way to go about making such a latch?
See also: Same question for Bedrock Edition (originally one question; separated upon request from others).
Question from user KnowledgeIsPower at gaming.stackexchange.com.
Answer:
I have managed to create a compact design for this so-called “SRT latch:”.
This circuit uses a T-flip-flop as its base. The T-flip-flop's output is used to activate pistons that complete a circuit from the corresponding S/R input to the toggle input. This effectively treats the S/R buttons as “conditional toggles.”.
This circuit is compact, simple, and uses its space effectively with a symmetrical layout. At its bare minimum, the footprint of this circuit is 5×3×2, excluding the space taken by the inputs and outputs.
Upon further thought, it turns out that this circuit is, in essence, a JK flip flop, the only difference being that the toggle function is controlled by a separate input, rather than with both inputs being on at once. This could theoretically render this design as one of the most compact JK flip flop designs in Minecraft.
This circuit is likely to work on MCBE, but has not yet been tested. I will transcribe this answer to the other question if I can confirm its functionality.
Answer from user KnowledgeIsPower at gaming.stackexchange.com.

SR latches and T-flip-flops are trivial circuitry in Minecraft redstone, but it appears that there is little to be found for a circuit that combines both, allowing for both SR and T functionality.
I envision an SR-T latch to have set, reset, and toggle inputs respectively, but all connected to the same memory cell. This means that the output can be controlled by setting it, resetting it, and toggling it all at once. Just like an SR latch, pressing S or R when the cell is already in that state should do nothing.
All of my circuitry so far has been "unclean" implementations, either a bodged wiring to add a toggle to an SR latch, or bodged wiring to add SR inputs to a T-flip-flop. What is the best way to go about making such a latch?
See also: Same question for Bedrock Edition (originally one question; separated upon request from others).
Question from user KnowledgeIsPower at gaming.stackexchange.com.
Answer:
I have managed to create a compact design for this so-called “SRT latch:”.
This circuit uses a T-flip-flop as its base. The T-flip-flop's output is used to activate pistons that complete a circuit from the corresponding S/R input to the toggle input. This effectively treats the S/R buttons as “conditional toggles.”.
This circuit is compact, simple, and uses its space effectively with a symmetrical layout. At its bare minimum, the footprint of this circuit is 5×3×2, excluding the space taken by the inputs and outputs.
Upon further thought, it turns out that this circuit is, in essence, a JK flip flop, the only difference being that the toggle function is controlled by a separate input, rather than with both inputs being on at once. This could theoretically render this design as one of the most compact JK flip flop designs in Minecraft.
This circuit is likely to work on MCBE, but has not yet been tested. I will transcribe this answer to the other question if I can confirm its functionality.
Answer from user KnowledgeIsPower at gaming.stackexchange.com.
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