The very basic Fiqh rule says:
الأصل في الأشياء الإباحة
The default state of things is permissible
Although usually "things" are meant to be food, drinks... etc. This rule can (probably with some caution) be applied to worship as well.
The Prophet (pbuh) said:
Narrated `Aisha:
The Prophet was asked, "What deeds are loved most by Allah?" He said,
"The most regular constant deeds even though they may be few." He
added, 'Don't take upon yourselves, except the deeds which are within
your ability."
حَدَّثَنِي مُحَمَّدُ بْنُ عَرْعَرَةَ، حَدَّثَنَا شُعْبَةُ، عَنْ سَعْدِ
بْنِ إِبْرَاهِيمَ، عَنْ أَبِي سَلَمَةَ، عَنْ عَائِشَةَ ـ رضى الله عنها
ـ أَنَّهَا قَالَتْ سُئِلَ النَّبِيُّ صلى الله عليه وسلم أَىُّ
الأَعْمَالِ أَحَبُّ إِلَى اللَّهِ قَالَ " أَدْوَمُهَا وَإِنْ قَلَّ
". وَقَالَ " اكْلَفُوا مِنَ الأَعْمَالِ مَا تُطِيقُونَ ".
[Sahih Bukhari], with many other context-similar Hadiths.
Obviously the Prophet didn't specify anything. Also he said:
Narrated Abu Huraira: Allah's Apostle said, "Allah said, 'I will
declare war against him who shows hostility to a pious worshipper of
Mine. And the most beloved things with which My slave comes nearer to
Me, is what I have enjoined upon him; and My slave keeps on coming
closer to Me through performing Nawafil (praying or doing extra deeds
besides what is obligatory) till I love him, so I become his sense of
hearing with which he hears, and his sense of sight with which he
sees, and his hand with which he grips, and his leg with which he
walks; and if he asks Me, I will give him, and if he asks My
protection (Refuge), I will protect him; (i.e. give him My Refuge) and
I do not hesitate to do anything as I hesitate to take the soul of the
believer, for he hates death, and I hate to disappoint him."
حَدَّثَنِي مُحَمَّدُ بْنُ عُثْمَانَ، حَدَّثَنَا خَالِدُ بْنُ مَخْلَدٍ،
حَدَّثَنَا سُلَيْمَانُ بْنُ بِلاَلٍ، حَدَّثَنِي شَرِيكُ بْنُ عَبْدِ
اللَّهِ بْنِ أَبِي نَمِرٍ، عَنْ عَطَاءٍ، عَنْ أَبِي هُرَيْرَةَ، قَالَ
قَالَ رَسُولُ اللَّهِ صلى الله عليه وسلم " إِنَّ اللَّهَ قَالَ مَنْ
عَادَى لِي وَلِيًّا فَقَدْ آذَنْتُهُ بِالْحَرْبِ، وَمَا تَقَرَّبَ
إِلَىَّ عَبْدِي بِشَىْءٍ أَحَبَّ إِلَىَّ مِمَّا افْتَرَضْتُ عَلَيْهِ،
وَمَا يَزَالُ عَبْدِي يَتَقَرَّبُ إِلَىَّ بِالنَّوَافِلِ حَتَّى
أُحِبَّهُ، فَإِذَا أَحْبَبْتُهُ كُنْتُ سَمْعَهُ الَّذِي يَسْمَعُ بِهِ،
وَبَصَرَهُ الَّذِي يُبْصِرُ بِهِ، وَيَدَهُ الَّتِي يَبْطُشُ بِهَا
وَرِجْلَهُ الَّتِي يَمْشِي بِهَا، وَإِنْ سَأَلَنِي لأُعْطِيَنَّهُ،
وَلَئِنِ اسْتَعَاذَنِي لأُعِيذَنَّهُ، وَمَا تَرَدَّدْتُ عَنْ شَىْءٍ
أَنَا فَاعِلُهُ تَرَدُّدِي عَنْ نَفْسِ الْمُؤْمِنِ، يَكْرَهُ الْمَوْتَ
وَأَنَا أَكْرَهُ مَسَاءَتَهُ ".
[Sahih Bukhari]
It's clear out from this Hadith that, if you are completed doing all obligatory worships, then doing extra worship is going to make Allah love you, but no specific sort of extra worship is mentioned.
Another Hadith I would like to mention is:
'Abdullah bin 'Amr (May Allah be pleased with them) reported: The
Messenger of Allah () said, "The Salat which is dearest to Allah is
that of (Prophet) Dawud; and As-Saum (the fasting) which is dearest to
Allah is that of (Prophet) Dawud. He used to sleep half the night, get
up to perform Salat for one-third of it, then sleep through the
remaining one-sixth of it; and he used to observe Saum on alternative
days."
[Al-Bukhari and Muslim].
وعن عبد الله بن عمرو بن العاص، رضي الله عنهما، أن رسول الله صلى الله
عليه وسلم ، قال: "أحب الصلاة إلى الله صلاة داود، وأحب الصيام إلى
الله صيام داود، كان ينام نصف الليل ويقوم ثلثه وينام سدسه ويصوم يومًا
ويفطر يومًا". ((متفق عليه)) .
[Riyad as-Salihin]
Despite the previous hadith, the Prophet (pbuh) was not reported to be fasting one day and not fasting the other day. So it's obvious that Allah did like something that the Prophet weren't doing, i.e, it's permitted.
However, keep in mind that these worships shouldn't be:
Exaggeration in a bad way, for example, not eating meat as an extra worship.
A "direct" contradiction of Sunnah, as not accepting Sunnah is not permissible.
As the Hadith says:
Narrated Anas bin Malik: A group of three men came to the houses of
the wives of the Prophet asking how the Prophet worshipped (Allah),
and when they were informed about that, they considered their worship
insufficient and said, "Where are we from the Prophet as his past and
future sins have been forgiven." Then one of them said, "I will offer
the prayer throughout the night forever." The other said, "I will fast
throughout the year and will not break my fast." The third said, "I
will keep away from the women and will not marry forever." Allah's
Apostle came to them and said, "Are you the same people who said
so-and-so? By Allah, I am more submissive to Allah and more afraid of
Him than you; yet I fast and break my fast, I do sleep and I also
marry women. So he who does not follow my tradition in religion, is
not from me (not one of my followers).
حَدَّثَنَا سَعِيدُ بْنُ أَبِي مَرْيَمَ، أَخْبَرَنَا مُحَمَّدُ بْنُ
جَعْفَرٍ، أَخْبَرَنَا حُمَيْدُ بْنُ أَبِي حُمَيْدٍ الطَّوِيلُ، أَنَّهُ
سَمِعَ أَنَسَ بْنَ مَالِكٍ ـ رضى الله عنه ـ يَقُولُ جَاءَ ثَلاَثَةُ
رَهْطٍ إِلَى بُيُوتِ أَزْوَاجِ النَّبِيِّ صلى الله عليه وسلم
يَسْأَلُونَ عَنْ عِبَادَةِ النَّبِيِّ صلى الله عليه وسلم فَلَمَّا
أُخْبِرُوا كَأَنَّهُمْ تَقَالُّوهَا فَقَالُوا وَأَيْنَ نَحْنُ مِنَ
النَّبِيِّ صلى الله عليه وسلم قَدْ غُفِرَ لَهُ مَا تَقَدَّمَ مِنْ
ذَنْبِهِ وَمَا تَأَخَّرَ. قَالَ أَحَدُهُمْ أَمَّا أَنَا فَإِنِّي
أُصَلِّي اللَّيْلَ أَبَدًا. وَقَالَ آخَرُ أَنَا أَصُومُ الدَّهْرَ
وَلاَ أُفْطِرُ. وَقَالَ آخَرُ أَنَا أَعْتَزِلُ النِّسَاءَ فَلاَ
أَتَزَوَّجُ أَبَدًا. فَجَاءَ رَسُولُ اللَّهِ صلى الله عليه وسلم
فَقَالَ " أَنْتُمُ الَّذِينَ قُلْتُمْ كَذَا وَكَذَا أَمَا وَاللَّهِ
إِنِّي لأَخْشَاكُمْ لِلَّهِ وَأَتْقَاكُمْ لَهُ، لَكِنِّي أَصُومُ
وَأُفْطِرُ، وَأُصَلِّي وَأَرْقُدُ وَأَتَزَوَّجُ النِّسَاءَ، فَمَنْ
رَغِبَ عَنْ سُنَّتِي فَلَيْسَ مِنِّي ".
[Sahih Bukhari] and [Sahih Muslim].
So to conclude: Yes it's generally permissible to do a custom extra worship not done by the Prophet and Ahl Al-Bayt, IF it's not exaggeration, contradictory to Sunnah, or, of course, containing something haram or something that leads to haram. And there are a lot of Hadiths about "فضائل الأعمال the preferred deeds" which Allah love most, so it'll be a good approach to try to do them.