As per the presumptive taxation scheme of section 44AE, the income of a taxpayer will be computed at the rate of Rs. 7,500 per goods vehicle per month or Rs. 1000 per ton of gross vehicle weight per month and in such a case can the taxpayer claim any further?

Under the normal provisions of the Income-tax Act, taxable business income will be computed after allowing deduction in respect of expenses which are deductible as per the Income-tax Act,1961 and after disallowing expenses which are not deductible as per the Income-tax Act, 1961.
In case of a person who is opting for the presumptive taxation scheme of sections 44AE, the provisions of allowance/disallowances as provided under the Income-tax Act,1961 will not apply and income computed at the presumptive rate :

a) Rs. 7,500 per month or part of the month for each goods carriage, during which the goods vehicle is owned by the assessee in the previous year. Part of the month would be considered as full month   (not applicable from A.Y 2019-20)
If the actual income is higher than the presumptive rate, then such higher income can be declared if the taxpayer wants to declare as such.
b) Rs. 7,500 per month or part of the month for each goods carriage (other than heavy goods vehicle) / Rs. 1000 per ton of gross vehicle weight per month or part of the month in case of heavy goods vehicle, during which the goods vehicle is owned by the assessee, in the previous year or actual amount earned whichever is higher. Part of the month would be considered as full month. (Applicable from A.Y 2019-20)

Heavy goods vehicles means any goods carriage vehicle whose gross vehicle weight exceeds 12000 kilograms.

Income computed at the presumptive rate as specified above will be the final income and no further deduction shall be allowed under sections 30 to 38 including depreciation and unabsorbed depreciation. However, in case of taxpayer, being a partnership firm deduction can be claimed on account of remuneration and interest paid to partners (computed as per the Income-tax Act,1961).