Is there any empirical upper limit for order of reaction?
The order of a reaction is an experimentally determined quantity and can be  positive, negative or fractional. The order need not be related to the stoichiometric coefficients, although sometimes it is. In some reactions it is not possible to define an order. There seems to be no reason therefore why the order cannot be greater than three; the iodate-iodine reduction (Dushman) reaction $\ce{IO3^- + 5I^- + 6H^+ -&gt; 3I2 + 3H2O}$ has the rate expression $r \approx \ce{[I^-][IO_3^-][H^+]^2  }$.

If the reaction is $aA+bB \rightarrow cC+dD$ then the rate is 

$$ r= - \frac{1}{a}\frac{d[A]}{dt} = \frac{1}{c}\frac{d[C]}{dt}= \cdots =k[A]^\alpha[B]^\beta[C]^\gamma \cdots$$

where the order n is $n=\alpha+\beta+\gamma$ and these need not be the same as a, b and c. 

If the rate expression is not of this form then it is hard to define an order; one familiar example is the chain reaction $\ce{H2 + Br2}$ where the experimentally determined rate law for the production of HBr has the form $\displaystyle r=\frac{k_2[\ce{H_2}][\ce{Br_2}]^{1/2}}{1+k_2'[\ce{HBr}]/[\ce{Br}]}$ where an overall order cannot be defined.

The order should not be confused with molecularity which describes the number of species reacting in a  postulated elementary reaction and which is always a small positive number. Effectively this means 1 or 2. A molecularity of 3 is not impossible but the chance of three  reactive species colliding at the same time is vanishingly small. In practice when a molecularity of 3 is suspected it is often found that in  subsequent experiments an intermediate is formed between of the two species which then reacts with the third at a slightly later time.