Is it possible? Yes.
Is it advisable? Maybe. If you have to ask, probably not. Some Austrian or Swiss mountain guides even advise against sleeping elevation increase of more than 300-500m per day, especially above 4000m. Here for example (german).
Now these guides tend to err on the side of caution as they are primarily intended for novices. I.e. 500m per day will be fine for basically everyone except for those with medical conditions, special medication (or those being reckless, not eating/drinking/sleeping enough etc.). That means that most of the population will probably be able to handle more than 500m per day.
Now, since you have to ask, you apparently don't know if you belong in that category or not. Maybe you can easily take 1000m a day, maybe you are in the 1% of people who get HACE at 4000m. With more experience you will be able to tell how much you can take.
I would advise against it if:
- you have known medical conditions related to your lung function etc.
- you take medication for blood pressure/lung function etc.
- you have experienced AMS (acute mountain sickness) at the target altitude
- you are "unfit" or the hike itself will put you to your limits.
- you are a heavy smoker
(incomplete list, just a few I can think of)
If you decide to do it, here are some precautions you can take:
- DO NOT GO ALONE!
- Always have an escape route, i.e. be able to descend at least 1000m quickly and do so if you experience AMS symptoms
- Drink enough (3-4l a day)
- Sleep an extra night at the same altitude before going higher (as recommended by the link above)
- Get enough sleep and eat sufficiently
- Ascend another 200-400m before going back down to you sleeping altitude
- Try to reduce the weight of your pack (20kg seems a lot)
- No alcohol