Concerning your question, the answer would depend on the observer.
An observer with 2 dimensional perception cannot intuit 3+ dimensions. Given some indirect evidence and the tools of math and logic, he might conclude a third dimension is likely. But if there is no indirect evidence of that dimension, to him it is unlikely. However if he is an observer with 3 dimensional perception ... and so on.
In the end, the total number and types of dimensions (temporal, spatial, etc.) is both unknown and unknowable. The error would be to say that other dimensions do not exist because an observer cannot perceive them directly or indirectly.
BTW, I often use that as an example why God's promise to Israel will never be broken (emphasis mine.)
And they shall teach no more every man his neighbour, and every man his brother, saying, Know the LORD: for they shall all know me, from the least of them unto the greatest of them, saith the LORD: for I will forgive their iniquity, and I will remember their sin no more.
Thus saith the LORD, which giveth the sun for a light by day, [and] the ordinances of the moon and of the stars for a light by night, which divideth the sea when the waves thereof roar; The LORD of hosts [is] his name: If those ordinances depart from before me, saith the LORD, [then] the seed of Israel also shall cease from being a nation before me for ever.
Thus saith the LORD; If heaven above can be measured, and the foundations of the earth searched out beneath, I will also cast off all the seed of Israel for all that they have done, saith the LORD. - Jer 31:33-37
ABSOLUTELY INDEED:
BTW, I often use that as an example why God’s promise to Israel will never be broken (emphasis mine.)
But this [shall be] the covenant that I will make with the house of Israel; After those days, saith the LORD, I will put my law in their inward parts, and write it in their hearts; and will be their God, and they shall be my people.
And they shall teach no more every man his neighbour, and every man his brother, saying, Know the LORD: for they shall all know me, from the least of them unto the greatest of them, saith the LORD: for I will forgive their iniquity, and I will remember their sin no more.
Thus saith the LORD, which giveth the sun for a light by day, [and] the ordinances of the moon and of the stars for a light by night, which divideth the sea when the waves thereof roar; The LORD of hosts [is] his name: If those ordinances depart from before me, saith the LORD, [then] the seed of Israel also shall cease from being a nation before me for ever.
Thus saith the LORD; If heaven above can be measured, and the foundations of the earth searched out beneath, I will also cast off all the seed of Israel for all that they have done, saith the LORD. - Jer 31:33-37