Hi I have a 2002 Corolla with an apexi, when driving it can start to splutter a bit and I have to put my accelerator down fully just to maintain the revs, then as the car slows I have to change down a gear or 2 and really give it revs just so it doesn't stall. Sometimes it stalls anyway and I have to change gears and let the clutch out to force it to start again. Often if it stalls when at low revs. If it stalls and am fully stopped, I have to put the clutch in and have my accelerator down fully when starting and that usually seems to fix the problem temporarily. Also it is slowly getting worse

I believe I would check for worn out motor mounts and transmission mounts.

may do but I think that it is in the carby
probably an accelerator pump jets blocked or failing to work properly
a carby overhaul may be in order

Check the fuel pressure with a gauge. The pump may be going bad

Sounds like lack of preventative maintenance

Spark Plugs every 3 years or 30 to 40,000 miles

You may have ignition coils failing

Clean MAF Sensor

Replace any O2 Sensors over 100,000 miles

Gas filter every 3 years

What is the make, the model and the year and engine type/size.

first check is the kick down switch working or not, as a first step, get in to the driver seat, don't switch on or start, press accelerator paddle slowly til end then depress and listen is it make a click sound or not, if not kick down switch could be faulty, this information for you to understand how the kick down switch working, when you drive the car did you depress and check the kick down working or not same as you did now? once again drive car and fully depress accelerator and check if not working you must get it in to the Mercedes workshop for right diagnose possibly faulty kick down switch in accelerator paddle, is this information helped you?

clogged fuel filter, or a short in your computer

I’m happy to assist further over the phone at https://www.6ya.com/expert/john_2c7bb9c157d0baa8

i had a 1996 corolla, the spark plug wires run through the top of the valve cover, pull them off and check for oil in the spark plug tubes, the seals go bad and oil leaks past the spark plugs and causes the engine to misfire

Most probably is the crank sensor under engine worn out. )0 % trobleshut starts here.
Einar Norway

Try moving up 1 grade of fuel, if you are using 87, put in 89. See if this helps.