Does our scriptures allow for having more than one unrelated ishtas?
No, there is "ONLY ONE ISHT". There is no concept of two isht. If anyone calls upon to say they have two isht, it's like sailing a river by keeping feet in two different boats.
Take example of Smart Sampradaya, thou all the Panchdevtas are worshipped equally by smarta upasakas. Yet they are asked to choose one out the five as Isht.
As you asked that can unrelated deities by isht?
So, Kali and Tara are both Mahavidyas. And both are the same tatwa expressed in two different forms. Yet, one can't worship both at a same time. Leave alone unrelated deities.
Yogini tantra, verifies the statement in the 2nd chapter,
या काली परमा विद्या सैव तारा न संशयः।
That Kali which is the Parma Vidya, is Tara herself, without any doubt.
So, a question arises, one can definetly worship both Mahavidyas, are both are same tatwa and even the shastra says same.
So, Yogini tantra further clarifies,
ताराशिष्यस्त्यजेत्कालीं कालीशिष्यस्तु तारिणीम्।
छिन्नामहिषमर्दिन्योह् कदाचित्पुजन स्मृतम।।
The sishya of Tara(the one dikshit in Tara mantra), must not worship Kali but should worship Tara, and likewise the shishya of Kali mustn't worship Tara but should worship Kali alone. If needed (under certain circumstances) he can worship Chinnamasta or Mahishamardini.
यदि वा पूजयेदेवि नान्यदेवानप्रपूजयेत।
कालीत्वेन च संभाव्य त्वन्याम् वा पूजयेच्छीवे।।
Oh, devi! If he wants to worship, then he must not worship others, rather worship Tara in the form of Kali and Kali in form of Tara by thinking so, and must worship them.
So, you see the statements clears that only the Isht must be worshiped and it has to be ONE, be it any of Kali or Tara in former case. And asks to see Isht even in vigrahas of other deities.
One such interesting anecdote is found in Tulsidasji's life too.
After he shifted to Varanasi, he once went to Vrindavana. There he saw viragaha of Shree Krishna, and he instantly said,
का वर्नु छबि आपकी, भले बने हो नाथ ।
तुलसी मस्तक तब नवे, जब धनुष बाण लो हाथ ।।
‘How shall I describe thy beauty, O Lord! But Tulsi will bow his head only when you take up bow and arrow in your hands’.
So, you see thou most of the people don't even see Ràm and Krishn as different, yet Tulsidasji was reluctant to bow down. He wanted to see his Ràm even in Krishn.
So,even thou the deities might be avatar of the same devta. Yet, people stick strictly to only any one. (That doesn't mean they can't worship others, but the Isht devta gets the highest priority).
Same happened with Ganapati Bhatt, he would never bow to other than Ganapti, when he came to Jaggannath, the lord had to appear as Ganapati. And even today the lord is dressed in Gajavesh. The anecdote of avatar Sureshwar, where mahadev goes as Indra to his devotee to test him. But, he says he shall ask boon only from Mahadeva, as he is his only isht.
Thus, its evident that Isht devta is only one.
Even if a person might have two ishtas, generally they're conjugal pairs like Shiva-Shakti, or Lakshmi-Narayanan
The conjugal pair can be isht only if the sampradaya allows. For example in Ramanujacharya sampradaya, the primary deity is Laxmi Narayana. But the basic point is, this are not seen as two isht. Instead they are taken as one, by Abheda.
Now, so what if our heart resonates with other deities too?
Those deities are called "Upasya devtas".And Upasya devtas can be any even those who got no link to Isht devta.
For example, Isht can be Kali, and upasaya can be Indra too for someone.
Now how to know, who is Isht or Upasya amongst two devtas,just see for whom your heart goes after.
It's like choosing between two closest of your frnds. The one whom you choose after thinking alot can be said as Isht, and the other one as Upasya.
Once a sadhu said this,
"It's always difficult to choose amongst deities,but it's useless digging 10 wells,since that's waste of energy and time, when you can dig a single well and reach the water.
Likewise worshipping 10 different deities is just wasting time, as only the Isht can take a person across this samsara, and give moksha."