It depends what you mean with "declare something halal or haram", and also "without a basis in the Quran and sunnah". An example might be, would analogical reasoning (qiyas) be considered a basis in the Quran/Sunnah?
Analogical reasoning is something that is not explicitly mentioned in the Quran or the Sunnah, but through the Quran and Sunnah, you draw some conclusions about a situation. Here is an example:
Narrated by Amr ibn al-'As:
I had a sexual dream on a cold night in the battle of Dhat as-Salasil. I was afraid, if I washed I would die. I, therefore, performed tayammum and led my companions in the dawn prayer. They mentioned that to the Messenger of Allah (ﷺ). He said: Amr, you led your companions is prayer while you were sexually defiled? I informed him of the cause which impeded me from washing. And I said: I heard Allah say: "Do not kill yourself, verily Allah is merciful to you." The Messenger of Allah (ﷺ) laughed and did not say anything.
Purification (Kitab Al-Taharah)
In this case we might interpret this saying that Amr ibn al-'As somehow "made something halal" that is why he prayed with his people without doing ghusl (he did tayammum instead). He made an analogy to the verse in the Quran which says: "do not kill yourself", and he thought that if he would take a bath, he might die. So it seems his companions had issues or questions about that, because there is no explicit verse or such that permits you to do what he did. So they mentioned it to the Prophet, who then asked Amr Ibn Al-'As if it is true that he prayed while he was "junub". He answered and explained why he did so and explained about the verse "Do not kill yourself...", the Prophet didn't seem to condemn him for his act.
فَقَالَ مُعَاذٌ لاَ أَرَاهُ عَلَى حَالٍ إِلاَّ كُنْتُ عَلَيْهَا . قَالَ فَقَالَ إِنَّ مُعَاذًا قَدْ سَنَّ لَكُمْ سُنَّةً كَذَلِكَ فَافْعَلُوا
Mu’adh then said; I shall follow the position (in the prayer when I join it) in which I find him (the prophet). He (the Prophet) then said: Mu'adh has introduced for you a sunnah, so do the same (when praying).
Sunan Abi Dawud,Prayer (Kitab Al-Salat)
When the Muslims prayed together in a congregation, they didn't do the same moves together, i.e some was doing ruku, while some was standing while some was doing sujud, some would be in first raka'a while others would be in the third. In this situation Mu’adh decided to follow the Prophet as he was praying, so if the Prophet would be in sujud, Mu'adh would also be in sujud. This is basically how we pray today. What we can see here is that Mu'adh had no basis in the Quran or Sunnah when he did this. The Prophet then informed the Muslims that all should do (in prayer) as Mu'adh did.
You will find similar incidents, for instance about Bilal praying two raka'a extra everytime he makes adhan, and a companion reading Surat Al-Ikhlas before every Surat in every raka'a (even though his companions said that he shouldn't do it):
(The Prophet said...) Why do you read this Surah particularly in every Rak'a ?" The man repiled, "I love this Surah." The Prophet (ﷺ) said, "Your love for this Surah will make you enter Paradise."
... and many more.
At least other companions somehow felt that there was no basis in the Quran or the Sunnah of the Prophet in these situations, therefore they always went to the Prophet informing him about these situations. And its clear that they was somehow upset that the persons did something which wasn't reveled in the Quran or directed by the Prophet. We notice that in many of these cases, the Prophet did not condemn the acts.
Now, the scholars have said that this was only allowed or not condemned in the time of the Prophet, while he was there and could inform them of the permissibility. While others interpret situations like these as a possibility of doing ijtihad, in different situations. This subject is highly connected to the definiton of bidah/innovation, which is a controversial topic in fiqh with many different opinions.