Is it possible for a deed, thing, thought etc to be both makrooh and haram at the same time?
No. one deed cannot be both. Because Makrooh is permitted (although is discouraged but anyway is permitted and has no sin or punishment) but Haram is forbidden and doing it has sin and punishment. It is contradiction that an action be both Makrooh and Haram because one deed cannot be both permitted and prohibited.
But sometimes one deed is not clearly mentioned as Haram or Makruh in Quran and Hadith. So it needs investigation in Hadith resources to be determined. So it is possible two different scholar have different view. For example one scholars says according to my research (Ijtihad) it is Haram and another scholars says according to my Ijtihad it is Makrooh. And this difference in Ijtihad is mostly because of different views on authenticity of a hadith. One scholar may consider a hadith authentic and another consider it weak. In fact both cannot be correct. But the followers of each scholar (Marja) should obey the fatwa of his own Marja. It is like when two doctor have different view about one patient. One doctor says surgery is needed and another says surgery is not needed and no one can determine who is correct because no one has the knowledge higher than them. The only one with higher knowledge is Imam Mahdi a.s. who is currently at Occultation and we do not have easy access to him.
Makrooh means Which is disliked (by Allah and his Rasul (Messenger)) and "Haram" means Strictly prohibited.
So, if a thing, thought or action is Haram, it is automatically also Makrooh.
But, if a thing, thought or action is Makrooh, it is not necessary that it will be also Haram. Most of the time, when we say an action is Makrooh, it is intended as lesser than Haram.
Allah knows best.
I think Anwar's answer has some good basics, but maybe he didn't explain his point well.
One could say for every deed and everything there are levels in shari'a which are placed between the two opposites: halal and haram.
Halal only means that something is allowed or permissible without explicitly explaining what we could call "the level of permission".
Haram means that something is forbidden, prohibited or illegal. So in this case we have a red line and a definite level this means if you do this you did something illegal if you went further you are still illegal ...
Now the levels are (this is only a simple scale starting with haram):
Haram > makrooh > mubah > mustahab ~ mandub
Here ">" could be replaced with "better" or equal, but in shari'a it is always understood as "better". And "~" could be understood as equal or more or less equal.
Note that makrooh, mubah etc. are levels of halal. Also note that mubah is one of the synonyms of halal in Arabic language, but in terms of fiqh only means that something is allowed and therefore it's level is less than something which is recommended.
As you asked about makroh it means: that it is frowned upon. This means doing it wouldn't be a sin but leaving it would be better. in Arabic language makrooh includes the root kariha كره which means hate, so something makrooh is hated so from a linguistic point of view there's a clear tendency to haram.
As I'm not aware of the shi'a fiqh so I must say that in some sunni madhabs there are statements about things being makrooh, which based on sahih hadiths should be perfectly fine (halal) this means at least mubah not makrooh. And especially those scholars who use the "Prohibition of evasive legal devices" often declare something halal as makrooh or haram if a reason or tendency to commit a sin through this is observable due to the practice of the people. As a matter which is considered as makrooh can be considered as something leading to haram or a sin. I think if you need information on how a ruling is concluded you can find a good explanation in Battle of Karbala's answer.
Now to your question I think from a linguistic perspective anything haram is makrooh, but anything makrooh is not haram. From a fiqh perspective we must do a clear cut, so anything which is makrooh is not haram per se. But if it leaded to haram based on the above mentioned rule it can be declared to be haram. For the special comment which is the background of your question I think a scholar may in his elaboration of a fatwa make a distinction of what is makrooh in an act or deed and what is haram usually if there's something haram he would deduce that the whole matter is haram. But of course if we put a (bad) deed or matter under a "microscope" we can find makrooh aspects and haram aspects beside mubah and maybe even mustahab aspects... so a coexistence isn't excluded in single parts of a deed, but a general view of the deed would give a definite fatwa about it!